subject:(Mapping class group)

Texas A&M University

1. Gustafson, Paul Prem. On the Property F Conjecture.

Degree: PhD, Mathematics, 2018, Texas A&M University

URL: http://hdl.handle.net/1969.1/173645

► This thesis solves the following question posed by Etingof, Rowell, and Witherspoon: Are the images of class="hilite">mapping class group representations associated to the modular category… (more)

Subjects/Keywords: TQFT; mapping class group; twisted Dijkgraaf–Witten; Property F conjecture

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APA (6^th Edition):

Gustafson, P. P. (2018). On the Property F Conjecture. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/173645

Chicago Manual of Style (16^th Edition):

Gustafson, Paul Prem. “On the Property F Conjecture.” 2018. Doctoral Dissertation, Texas A&M University. Accessed March 08, 2021. http://hdl.handle.net/1969.1/173645.

MLA Handbook (7^th Edition):

Gustafson, Paul Prem. “On the Property F Conjecture.” 2018. Web. 08 Mar 2021.

Vancouver:

Gustafson PP. On the Property F Conjecture. [Internet] [Doctoral dissertation]. Texas A&M University; 2018. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1969.1/173645.

Council of Science Editors:

Gustafson PP. On the Property F Conjecture. [Doctoral Dissertation]. Texas A&M University; 2018. Available from: http://hdl.handle.net/1969.1/173645

University of Illinois – Chicago

2. Durham, Matthew G. The Coarse Geometry of the Teichmuller Metric: A Quasiisometry Model and the Actions of Finite Groups.

Degree: 2014, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/19007

► Let S be a surface of finite type and T(S) its Teichmuller space. In the first chapter of the thesis, we build a graph called… (more)

Subjects/Keywords: Geometric group theory; Teichmuller space; mapping class groups; Nielsen realization

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APA (6^th Edition):

Durham, M. G. (2014). The Coarse Geometry of the Teichmuller Metric: A Quasiisometry Model and the Actions of Finite Groups. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/19007

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Durham, Matthew G. “The Coarse Geometry of the Teichmuller Metric: A Quasiisometry Model and the Actions of Finite Groups.” 2014. Thesis, University of Illinois – Chicago. Accessed March 08, 2021. http://hdl.handle.net/10027/19007.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Durham, Matthew G. “The Coarse Geometry of the Teichmuller Metric: A Quasiisometry Model and the Actions of Finite Groups.” 2014. Web. 08 Mar 2021.

Vancouver:

Durham MG. The Coarse Geometry of the Teichmuller Metric: A Quasiisometry Model and the Actions of Finite Groups. [Internet] [Thesis]. University of Illinois – Chicago; 2014. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10027/19007.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Durham MG. The Coarse Geometry of the Teichmuller Metric: A Quasiisometry Model and the Actions of Finite Groups. [Thesis]. University of Illinois – Chicago; 2014. Available from: http://hdl.handle.net/10027/19007

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Boston College

3. Vlamis, Nicholas George. Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces.

Degree: PhD, Mathematics, 2015, Boston College

URL: http://dlib.bc.edu/islandora/object/bc-ir:104137

► The first part of this dissertation is on the quasiconformal homogeneity of surfaces. In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the… (more)

Subjects/Keywords: hyperbolic manifold; identities; mapping class group; orthospectrum; quasiconformal maps

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APA (6^th Edition):

Vlamis, N. G. (2015). Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces. (Doctoral Dissertation). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:104137

Chicago Manual of Style (16^th Edition):

Vlamis, Nicholas George. “Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces.” 2015. Doctoral Dissertation, Boston College. Accessed March 08, 2021. http://dlib.bc.edu/islandora/object/bc-ir:104137.

MLA Handbook (7^th Edition):

Vlamis, Nicholas George. “Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces.” 2015. Web. 08 Mar 2021.

Vancouver:

Vlamis NG. Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces. [Internet] [Doctoral dissertation]. Boston College; 2015. [cited 2021 Mar 08]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:104137.

Council of Science Editors:

Vlamis NG. Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces. [Doctoral Dissertation]. Boston College; 2015. Available from: http://dlib.bc.edu/islandora/object/bc-ir:104137

University of Oxford

4. Hume, David S. Embeddings of infinite groups into Banach spaces.

Degree: PhD, 2013, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581386

► In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and class="hilite">mapping class groups, especially with respect to the difficulty… (more)

Subjects/Keywords: 515.732; Mathematics; group theory; metric geometry; hyperbolic; relatively hyperbolic; mapping class group

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APA (6^th Edition):

Hume, D. S. (2013). Embeddings of infinite groups into Banach spaces. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581386

Chicago Manual of Style (16^th Edition):

Hume, David S. “Embeddings of infinite groups into Banach spaces.” 2013. Doctoral Dissertation, University of Oxford. Accessed March 08, 2021. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581386.

MLA Handbook (7^th Edition):

Hume, David S. “Embeddings of infinite groups into Banach spaces.” 2013. Web. 08 Mar 2021.

Vancouver:

Hume DS. Embeddings of infinite groups into Banach spaces. [Internet] [Doctoral dissertation]. University of Oxford; 2013. [cited 2021 Mar 08]. Available from: http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581386.

Council of Science Editors:

Hume DS. Embeddings of infinite groups into Banach spaces. [Doctoral Dissertation]. University of Oxford; 2013. Available from: http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581386

University of Illinois – Urbana-Champaign

5. Mousley, Sarah C. Boundaries and hierarchically hyperbolic spaces.

Degree: PhD, Mathematics, 2019, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/104790

► Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we… (more)

Subjects/Keywords: Teichmuller space; mapping class group; right-angled Artin group; hierarchically hyperbolic; limit set

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APA (6^th Edition):

Mousley, S. C. (2019). Boundaries and hierarchically hyperbolic spaces. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/104790

Chicago Manual of Style (16^th Edition):

Mousley, Sarah C. “Boundaries and hierarchically hyperbolic spaces.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 08, 2021. http://hdl.handle.net/2142/104790.

MLA Handbook (7^th Edition):

Mousley, Sarah C. “Boundaries and hierarchically hyperbolic spaces.” 2019. Web. 08 Mar 2021.

Vancouver:

Mousley SC. Boundaries and hierarchically hyperbolic spaces. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/2142/104790.

Council of Science Editors:

Mousley SC. Boundaries and hierarchically hyperbolic spaces. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/104790

6. Disarlo, Valentina. Combinatorial methods in Teichmüller theory : Méthodes combinatoires en théorie de Teichmüller.

Degree: Docteur es, Mathématiques, 2013, Strasbourg; Scuola normale superiore (Pise, Italie)

URL: http://www.theses.fr/2013STRAD017

►

Dans cette thèse nous étudions certains propriétés combinatoires et géométriques des complexes d'arcs des surfaces de type fini. Nous démontrons que le groupe d'automorphisme du… (more)

Subjects/Keywords: Mapping class group; Espaces de Teichmueller; Complexe des arcs; Mapping class groups; Teichmueller space; Arc complex; 511.6; 514.2

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APA (6^th Edition):

Disarlo, V. (2013). Combinatorial methods in Teichmüller theory : Méthodes combinatoires en théorie de Teichmüller. (Doctoral Dissertation). Strasbourg; Scuola normale superiore (Pise, Italie). Retrieved from http://www.theses.fr/2013STRAD017

Chicago Manual of Style (16^th Edition):

Disarlo, Valentina. “Combinatorial methods in Teichmüller theory : Méthodes combinatoires en théorie de Teichmüller.” 2013. Doctoral Dissertation, Strasbourg; Scuola normale superiore (Pise, Italie). Accessed March 08, 2021. http://www.theses.fr/2013STRAD017.

MLA Handbook (7^th Edition):

Disarlo, Valentina. “Combinatorial methods in Teichmüller theory : Méthodes combinatoires en théorie de Teichmüller.” 2013. Web. 08 Mar 2021.

Vancouver:

Disarlo V. Combinatorial methods in Teichmüller theory : Méthodes combinatoires en théorie de Teichmüller. [Internet] [Doctoral dissertation]. Strasbourg; Scuola normale superiore (Pise, Italie); 2013. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2013STRAD017.

Council of Science Editors:

Disarlo V. Combinatorial methods in Teichmüller theory : Méthodes combinatoires en théorie de Teichmüller. [Doctoral Dissertation]. Strasbourg; Scuola normale superiore (Pise, Italie); 2013. Available from: http://www.theses.fr/2013STRAD017

Université de Grenoble

7. Korinman, Julien. Sur les représentations quantiques des groupes modulaires des surfaces : On the quantum representations of class="hilite">mapping class groups of surfaces.

Degree: Docteur es, Mathématiques, 2014, Université de Grenoble

URL: http://www.theses.fr/2014GRENM070

►

Cette thèse porte sur l'étude de certaines familles de représentations projectives des groupes modulaires de surfaces issues de théories topologiques quantiques de champs. Les résultats… (more)

Subjects/Keywords: Topologie; Algèbre; TQFT; Noeuds; Topology; Algebra; TQFT; Knot; Mapping class group; 510

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APA (6^th Edition):

Korinman, J. (2014). Sur les représentations quantiques des groupes modulaires des surfaces : On the quantum representations of mapping class groups of surfaces. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2014GRENM070

Chicago Manual of Style (16^th Edition):

Korinman, Julien. “Sur les représentations quantiques des groupes modulaires des surfaces : On the quantum representations of mapping class groups of surfaces.” 2014. Doctoral Dissertation, Université de Grenoble. Accessed March 08, 2021. http://www.theses.fr/2014GRENM070.

MLA Handbook (7^th Edition):

Korinman, Julien. “Sur les représentations quantiques des groupes modulaires des surfaces : On the quantum representations of mapping class groups of surfaces.” 2014. Web. 08 Mar 2021.

Vancouver:

Korinman J. Sur les représentations quantiques des groupes modulaires des surfaces : On the quantum representations of mapping class groups of surfaces. [Internet] [Doctoral dissertation]. Université de Grenoble; 2014. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2014GRENM070.

Council of Science Editors:

Korinman J. Sur les représentations quantiques des groupes modulaires des surfaces : On the quantum representations of mapping class groups of surfaces. [Doctoral Dissertation]. Université de Grenoble; 2014. Available from: http://www.theses.fr/2014GRENM070

University of Toronto

8. Verberne, Yvon Louise Maria. Pseudo-Anosov Homeomorphisms Constructed using Positive Dehn Twists.

Degree: PhD, 2020, University of Toronto

URL: http://hdl.handle.net/1807/101022

► The class="hilite">mapping class group is the group orientation preserving homeomorphisms of a surface up to isotopy. The class="hilite">mapping class group encodes information about the symmetries… (more)

Subjects/Keywords: Algebra; Geometric group theory; Geometry; Mapping class groups; Pseudo-Anosov; Topology; 0642

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APA (6^th Edition):

Verberne, Y. L. M. (2020). Pseudo-Anosov Homeomorphisms Constructed using Positive Dehn Twists. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/101022

Chicago Manual of Style (16^th Edition):

Verberne, Yvon Louise Maria. “Pseudo-Anosov Homeomorphisms Constructed using Positive Dehn Twists.” 2020. Doctoral Dissertation, University of Toronto. Accessed March 08, 2021. http://hdl.handle.net/1807/101022.

MLA Handbook (7^th Edition):

Verberne, Yvon Louise Maria. “Pseudo-Anosov Homeomorphisms Constructed using Positive Dehn Twists.” 2020. Web. 08 Mar 2021.

Vancouver:

Verberne YLM. Pseudo-Anosov Homeomorphisms Constructed using Positive Dehn Twists. [Internet] [Doctoral dissertation]. University of Toronto; 2020. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1807/101022.

Council of Science Editors:

Verberne YLM. Pseudo-Anosov Homeomorphisms Constructed using Positive Dehn Twists. [Doctoral Dissertation]. University of Toronto; 2020. Available from: http://hdl.handle.net/1807/101022

9. Ackermann, Robert. On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies.

Degree: 2014, University of California – eScholarship, University of California

URL: http://www.escholarship.org/uc/item/4g92n22s

► In 1988, William Thurston announced the completion of a classification of surface automorphisms into three types up to isotopy: periodic, reducible, and pseudo-Anosov. The most… (more)

Subjects/Keywords: Mathematics; compression body; dilatation; mapping class group; Perron-Frobenius; pseudo-Anosov; symplectic

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APA (6^th Edition):

Ackermann, R. (2014). On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies. (Thesis). University of California – eScholarship, University of California. Retrieved from http://www.escholarship.org/uc/item/4g92n22s

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ackermann, Robert. “On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies.” 2014. Thesis, University of California – eScholarship, University of California. Accessed March 08, 2021. http://www.escholarship.org/uc/item/4g92n22s.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ackermann, Robert. “On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies.” 2014. Web. 08 Mar 2021.

Vancouver:

Ackermann R. On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies. [Internet] [Thesis]. University of California – eScholarship, University of California; 2014. [cited 2021 Mar 08]. Available from: http://www.escholarship.org/uc/item/4g92n22s.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ackermann R. On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies. [Thesis]. University of California – eScholarship, University of California; 2014. Available from: http://www.escholarship.org/uc/item/4g92n22s

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Minnesota

10. Nayak, Guruprasad. Learning with Weak Supervision for Land Cover class="hilite">Mapping Problems.

Degree: PhD, Computer Science, 2020, University of Minnesota

URL: http://hdl.handle.net/11299/213091

► Land cover class="hilite">mapping is the task of generating maps of land use globally across time. The recent decades have seen an increasing availability of public… (more)

▼ Land cover class="hilite">mapping is the task of generating maps of land use globally across time. The recent decades have seen an increasing availability of public satellite data sets with observations of the Earth at regular intervals of space and time. This coupled with the advances in machine learning and high performance computing provide an opportunity to automate the land cover class="hilite">mapping problem at scale. However, the availability of labeled data to train predictive models in this application is very limited, especially in the developing regions of the world, where accurate land cover maps are necessary for effective management of natural resources to sustain the rapid population growth in these regions. The need for labeled samples is further increased by: (1) Heterogeneity of land cover classes across space and time; (2) Increasing complexity of state-of-the-art predictive models and (3) Lack of sufficient samples at the required spatial and temporal resolutions. Since paucity of labeled data is a major problem in this domain, traditional machine learning algorithms that only rely on exact labeled data (strong supervision) have limited performance. This thesis investigates the use of weak supervision to mitigate the problem of not having sufficient samples with exact labels. In a weakly-supervised learning scenario, you have very few training samples that have exact labels corresponding to the target variable. However, you have plenty of weakly-labeled instances i.e you have an imperfect version of the target variable for these instances. The idea is that, by modeling the imperfection in the weak labels, we can mitigate the lack of (strongly-labeled) training data. We study three commonly-occurring sources of weak supervision for the land cover class="hilite">mapping problem: (1) Ordinal labels as weak supervision for regression (WORD); (2) Group-level labels as weak supervision for binary classification (WeaSL); and (3) Group-level labels with group-level features as weak supervision for binary classification (MultiRes). In each of these cases, we show that modeling the inexact nature of the weak supervision enables us to mitigate the lack of strong supervision. By extensive experiments on multiple data sets, we show that use of weak supervision (1) increases the generalizability of models trained with only strong supervision and (2) enables the use of more complex predictive models. In addition, since weak supervision is available in plenty, they provide a better representation of the class imbalance, when present in the population. WORD and WeaSL demonstrably optimize the performance of the model for rarity using weak supervision. Finally, although the data sets used in this thesis mainly come from the land cover problems of burned area class="hilite">mapping and urban class="hilite">mapping, the methods developed in this thesis are applicable to other domains as well, where similar forms of weak labels are available as demonstrated by experiments on data sets from other domains like natural language processing.

Subjects/Keywords: Class imbalance; Group Labels; Land cover mapping; Ordinal Labels; Semi-supervised Learning; Weak Supervision

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APA (6^th Edition):

Nayak, G. (2020). Learning with Weak Supervision for Land Cover Mapping Problems. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/213091

Chicago Manual of Style (16^th Edition):

Nayak, Guruprasad. “Learning with Weak Supervision for Land Cover Mapping Problems.” 2020. Doctoral Dissertation, University of Minnesota. Accessed March 08, 2021. http://hdl.handle.net/11299/213091.

MLA Handbook (7^th Edition):

Nayak, Guruprasad. “Learning with Weak Supervision for Land Cover Mapping Problems.” 2020. Web. 08 Mar 2021.

Vancouver:

Nayak G. Learning with Weak Supervision for Land Cover Mapping Problems. [Internet] [Doctoral dissertation]. University of Minnesota; 2020. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/11299/213091.

Council of Science Editors:

Nayak G. Learning with Weak Supervision for Land Cover Mapping Problems. [Doctoral Dissertation]. University of Minnesota; 2020. Available from: http://hdl.handle.net/11299/213091

University of Maryland

11. Chuysurichay, Sompong. Positive Rational Strong Shift Equivalence and The class="hilite">Mapping Class Group of A Shift of Finite Type.

Degree: Mathematics, 2011, University of Maryland

URL: http://hdl.handle.net/1903/11674

► This thesis studies two independent topics in symbolic dynamics, the positive rational strong shift equivalence and the class="hilite">mapping class group of a shift of finite… (more)

Subjects/Keywords: Mathematics; automorphism; flow equivalence; mapping class group; shift of finite type; simplex; strong shift equivalence

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APA (6^th Edition):

Chuysurichay, S. (2011). Positive Rational Strong Shift Equivalence and The Mapping Class Group of A Shift of Finite Type. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/11674

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chuysurichay, Sompong. “Positive Rational Strong Shift Equivalence and The Mapping Class Group of A Shift of Finite Type.” 2011. Thesis, University of Maryland. Accessed March 08, 2021. http://hdl.handle.net/1903/11674.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chuysurichay, Sompong. “Positive Rational Strong Shift Equivalence and The Mapping Class Group of A Shift of Finite Type.” 2011. Web. 08 Mar 2021.

Vancouver:

Chuysurichay S. Positive Rational Strong Shift Equivalence and The Mapping Class Group of A Shift of Finite Type. [Internet] [Thesis]. University of Maryland; 2011. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1903/11674.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chuysurichay S. Positive Rational Strong Shift Equivalence and The Mapping Class Group of A Shift of Finite Type. [Thesis]. University of Maryland; 2011. Available from: http://hdl.handle.net/1903/11674

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

12. Cooper, James Michael. Two mod-p Johnson filtrations.

Degree: PhD, Natural Sciences, 2014, Rice University

URL: http://hdl.handle.net/1911/76394

► We consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying these series to definitions of Dennis Johnson's filtration of… (more)

Subjects/Keywords: Geometric topology; Group theory; Mapping class groups

…particularly interesting algebraic invariant of a surface is its mapping class group. We write M odg… …1 for the mapping class group of an orientable surface of genus g with 1 boundary… …mapping class group appears in many areas of mathematics as an important object of study. Still… …within the realm of topology, the mapping class group is intimately related to the study of 3… …mapping class group naturally arises as an object of interest, too. For instance, the mapping…

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APA (6^th Edition):

Cooper, J. M. (2014). Two mod-p Johnson filtrations. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/76394

Chicago Manual of Style (16^th Edition):

Cooper, James Michael. “Two mod-p Johnson filtrations.” 2014. Doctoral Dissertation, Rice University. Accessed March 08, 2021. http://hdl.handle.net/1911/76394.

MLA Handbook (7^th Edition):

Cooper, James Michael. “Two mod-p Johnson filtrations.” 2014. Web. 08 Mar 2021.

Vancouver:

Cooper JM. Two mod-p Johnson filtrations. [Internet] [Doctoral dissertation]. Rice University; 2014. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/1911/76394.

Council of Science Editors:

Cooper JM. Two mod-p Johnson filtrations. [Doctoral Dissertation]. Rice University; 2014. Available from: http://hdl.handle.net/1911/76394

University of Arizona

13. Konstantinou, Panagiota. Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the class="hilite">Mapping Class Group.

Degree: 2006, University of Arizona

URL: http://hdl.handle.net/10150/193713

► In this paper we consider the action of the class="hilite">mapping class group of a surface on the space of homomorphisms from the fundamental group of… (more)

Subjects/Keywords: representation varieties; mapping class group; teichmuller space; ergodic action

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APA (6^th Edition):

Konstantinou, P. (2006). Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/193713

Chicago Manual of Style (16^th Edition):

Konstantinou, Panagiota. “Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group. ” 2006. Doctoral Dissertation, University of Arizona. Accessed March 08, 2021. http://hdl.handle.net/10150/193713.

MLA Handbook (7^th Edition):

Konstantinou, Panagiota. “Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group. ” 2006. Web. 08 Mar 2021.

Vancouver:

Konstantinou P. Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group. [Internet] [Doctoral dissertation]. University of Arizona; 2006. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10150/193713.

Council of Science Editors:

Konstantinou P. Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group. [Doctoral Dissertation]. University of Arizona; 2006. Available from: http://hdl.handle.net/10150/193713

Université de Grenoble

14. Nguyen, Maxime. Groupes modulaires et groupes d'automorphismes de complexes de surfaces de type infini : class="hilite">Mapping class groups and automorphisms of complexes of surfaces of infinite type.

Degree: Docteur es, Mathématiques, 2012, Université de Grenoble

URL: http://www.theses.fr/2012GRENM102

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Soit sigma g,n une surface orientable de genre g avec n trous. Le groupe modulaire de sigma g,n agit sur divers complexes, comme le complexe… (more)

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Soit sigma g,n une surface orientable de genre g avec n trous. Le groupe modulaire de sigma g,n agit sur divers complexes, comme le complexe de courbes et le complexe de décomposition en pantalons. Il a été prouvé, selon une approche initialement établie par Ivanov, que le groupe d'automorphismes de chacun de ces complexes est isomorphe au groupe modulaire. Cela implique notamment que le groupe des automorphismes extérieurs d'un sous-groupe d'indice fini du groupe modulaire est fini. Le but de cette thèse est de démontrer un résultat similaire s'appliquant à des surfaces de type infini de genre zéro. Pour cela, on définit un groupe modulaire asymptotique de ces surfaces, puis un complexe cellulaire localement infini sur lequel le groupe modulaire agit naturellement. On fait apparaitre des propriétés du groupe des automorphismes de chaque complexe en faisant agir les automorphismes sur des graphes auxiliaires. Le premier groupe modulaire étudiée est isomorphe au groupe de Thompson T. Le second est une extension du groupe modulaire universel de genre zéro.

Let sigma g,n be an orientable surface of genus g with n punctures. The class="hilite">mapping class group of sigma g,n acts on several complexes, for instance the curve complex or the pants complex of the surface. It is proved that the automorphism group of each of these complexes are isomorphic to the class="hilite">mapping class group. This implies in particular that the group of outer automorphisms of a finite index subgroup is finite. The purpose of this thesis is to prove a similar result on some surfaces of infinite type and genus zero. For this, we define an asymptotic class="hilite">mapping class group of these surfaces, and then a locally infinite cellular complex where the class="hilite">mapping class group acts naturally. It brings up some properties of the automorphism group of each cellular complex by making automorphisms act on auxiliary graphs. The first studied asymptotic class="hilite">mapping class group is isomorphic to the Thompson group T. The second one is an extension of the universal class="hilite">mapping class group of genus zero.

Advisors/Committee Members: Funar, Louis (thesis director).

Subjects/Keywords: Groupe modulaire; Complexe de pantalons; Surface de type infini; Groupe de Thompson; Mapping class group; Pants complex; Surface of infinite type; Thompson group; 510

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APA (6^th Edition):

Nguyen, M. (2012). Groupes modulaires et groupes d'automorphismes de complexes de surfaces de type infini : Mapping class groups and automorphisms of complexes of surfaces of infinite type. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2012GRENM102

Chicago Manual of Style (16^th Edition):

Nguyen, Maxime. “Groupes modulaires et groupes d'automorphismes de complexes de surfaces de type infini : Mapping class groups and automorphisms of complexes of surfaces of infinite type.” 2012. Doctoral Dissertation, Université de Grenoble. Accessed March 08, 2021. http://www.theses.fr/2012GRENM102.

MLA Handbook (7^th Edition):

Nguyen, Maxime. “Groupes modulaires et groupes d'automorphismes de complexes de surfaces de type infini : Mapping class groups and automorphisms of complexes of surfaces of infinite type.” 2012. Web. 08 Mar 2021.

Vancouver:

Nguyen M. Groupes modulaires et groupes d'automorphismes de complexes de surfaces de type infini : Mapping class groups and automorphisms of complexes of surfaces of infinite type. [Internet] [Doctoral dissertation]. Université de Grenoble; 2012. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2012GRENM102.

Council of Science Editors:

Nguyen M. Groupes modulaires et groupes d'automorphismes de complexes de surfaces de type infini : Mapping class groups and automorphisms of complexes of surfaces of infinite type. [Doctoral Dissertation]. Université de Grenoble; 2012. Available from: http://www.theses.fr/2012GRENM102

15. HU HENGNAN. Identities on Hyperbolic Surfaces, Group Actions and the Markoff-Hurwitz Equations.

Degree: 2013, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/48648

Subjects/Keywords: McShane's identity; Roger's dilogarithm; Mapping class group; Character variety; Coxeter group; Hurwitz equation

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APA (6^th Edition):

HENGNAN, H. (2013). Identities on Hyperbolic Surfaces, Group Actions and the Markoff-Hurwitz Equations. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/48648

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

HENGNAN, HU. “Identities on Hyperbolic Surfaces, Group Actions and the Markoff-Hurwitz Equations.” 2013. Thesis, National University of Singapore. Accessed March 08, 2021. http://scholarbank.nus.edu.sg/handle/10635/48648.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

HENGNAN, HU. “Identities on Hyperbolic Surfaces, Group Actions and the Markoff-Hurwitz Equations.” 2013. Web. 08 Mar 2021.

Vancouver:

HENGNAN H. Identities on Hyperbolic Surfaces, Group Actions and the Markoff-Hurwitz Equations. [Internet] [Thesis]. National University of Singapore; 2013. [cited 2021 Mar 08]. Available from: http://scholarbank.nus.edu.sg/handle/10635/48648.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

HENGNAN H. Identities on Hyperbolic Surfaces, Group Actions and the Markoff-Hurwitz Equations. [Thesis]. National University of Singapore; 2013. Available from: http://scholarbank.nus.edu.sg/handle/10635/48648

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Louisiana State University

16. Childers, Leah R. Subgroups of the Torelli group.

Degree: PhD, Applied Mathematics, 2010, Louisiana State University

URL: etd-05252010-101928 ; https://digitalcommons.lsu.edu/gradschool_dissertations/536

► Let Mod(Sg) be the class="hilite">mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces… (more)

Subjects/Keywords: symmetric separating curve complex; Torelli group; mapping class group; symmetric Torelli group; simply intersecting pair maps; curve complex; symmetric mapping class group

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APA (6^th Edition):

Childers, L. R. (2010). Subgroups of the Torelli group. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-05252010-101928 ; https://digitalcommons.lsu.edu/gradschool_dissertations/536

Chicago Manual of Style (16^th Edition):

Childers, Leah R. “Subgroups of the Torelli group.” 2010. Doctoral Dissertation, Louisiana State University. Accessed March 08, 2021. etd-05252010-101928 ; https://digitalcommons.lsu.edu/gradschool_dissertations/536.

MLA Handbook (7^th Edition):

Childers, Leah R. “Subgroups of the Torelli group.” 2010. Web. 08 Mar 2021.

Vancouver:

Childers LR. Subgroups of the Torelli group. [Internet] [Doctoral dissertation]. Louisiana State University; 2010. [cited 2021 Mar 08]. Available from: etd-05252010-101928 ; https://digitalcommons.lsu.edu/gradschool_dissertations/536.

Council of Science Editors:

Childers LR. Subgroups of the Torelli group. [Doctoral Dissertation]. Louisiana State University; 2010. Available from: etd-05252010-101928 ; https://digitalcommons.lsu.edu/gradschool_dissertations/536

17. Kutluhan, Johanna Ceres Isabel Mangahas. A Recipe for Short-word Pseudo-Anosovs, and Group Growth.

Degree: PhD, Mathematics, 2010, University of Michigan

URL: http://hdl.handle.net/2027.42/77720

► The dissertation solves the short-word pseudo-Anosov problem posed by Fujiwara. Given any generating set of any pseudo-Anosov-containing subgroup of the class="hilite">mapping class group of a… (more)

Subjects/Keywords: Mapping Class Group; Pseudo-Anosov; Curve Complex; Mathematics; Science

…separate motivation for Theorem I.1 is its utility for quantifying the mapping 4 class group… …first presents basic definitions around the mapping class group and curve complex; the second… …Mapping class group and curve complex Throughout, we consider only oriented surfaces whose… …definitions of the mapping class group. Given a surface S, its mapping class group Mod(S)… …the mapping class group to require that homeomorphisms and isotopy fix ∂S pointwise…

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APA (6^th Edition):

Kutluhan, J. C. I. M. (2010). A Recipe for Short-word Pseudo-Anosovs, and Group Growth. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/77720

Chicago Manual of Style (16^th Edition):

Kutluhan, Johanna Ceres Isabel Mangahas. “A Recipe for Short-word Pseudo-Anosovs, and Group Growth.” 2010. Doctoral Dissertation, University of Michigan. Accessed March 08, 2021. http://hdl.handle.net/2027.42/77720.

MLA Handbook (7^th Edition):

Kutluhan, Johanna Ceres Isabel Mangahas. “A Recipe for Short-word Pseudo-Anosovs, and Group Growth.” 2010. Web. 08 Mar 2021.

Vancouver:

Kutluhan JCIM. A Recipe for Short-word Pseudo-Anosovs, and Group Growth. [Internet] [Doctoral dissertation]. University of Michigan; 2010. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/2027.42/77720.

Council of Science Editors:

Kutluhan JCIM. A Recipe for Short-word Pseudo-Anosovs, and Group Growth. [Doctoral Dissertation]. University of Michigan; 2010. Available from: http://hdl.handle.net/2027.42/77720

Universitat Autònoma de Barcelona

18. Riba Garcia, Ricard. Trivial 2-cocycles for invariants of mod p homology spheres and Perron's conjecture.

Degree: Departament de Matemàtiques, 2018, Universitat Autònoma de Barcelona

URL: http://hdl.handle.net/10803/664243

► The main objective of this thesis is the study Perron's conjecture. This conjecture affirms that some function on the group of Torelli mod p, with… (more)

Subjects/Keywords: 3-varietats; 3-variedades; 3-mamifolds; Grup de classes d'aplicacions; Grupo de clases de aplicaciones; Mapping class group; Invariants topològics; Invariantes topológicos; Topological invariants; Ciències Experimentals; 515.1

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APA (6^th Edition):

Riba Garcia, R. (2018). Trivial 2-cocycles for invariants of mod p homology spheres and Perron's conjecture. (Thesis). Universitat Autònoma de Barcelona. Retrieved from http://hdl.handle.net/10803/664243

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Riba Garcia, Ricard. “Trivial 2-cocycles for invariants of mod p homology spheres and Perron's conjecture.” 2018. Thesis, Universitat Autònoma de Barcelona. Accessed March 08, 2021. http://hdl.handle.net/10803/664243.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Riba Garcia, Ricard. “Trivial 2-cocycles for invariants of mod p homology spheres and Perron's conjecture.” 2018. Web. 08 Mar 2021.

Vancouver:

Riba Garcia R. Trivial 2-cocycles for invariants of mod p homology spheres and Perron's conjecture. [Internet] [Thesis]. Universitat Autònoma de Barcelona; 2018. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10803/664243.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Riba Garcia R. Trivial 2-cocycles for invariants of mod p homology spheres and Perron's conjecture. [Thesis]. Universitat Autònoma de Barcelona; 2018. Available from: http://hdl.handle.net/10803/664243

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

19. Pankau, Joshua Charles. On stretch factors of pseudo-Anosov maps.

Degree: 2018, University of California – eScholarship, University of California

URL: http://www.escholarship.org/uc/item/5q48t1cj

► In 1974, Thurston proved that, up to isotopy, every automorphism of closed orientable surface is either periodic, reducible, or pseudo-Anosov. The latter case has lead… (more)

Subjects/Keywords: Mathematics; mapping class group; pseudo-Anosov; salem numbers; thurston; topology

…Contents 1 Introduction 1 2 The Mapping Class Group 5 2.1 2.2 2.3 Curves on Surfaces… …known as the mapping class group of a surface, first appeared in the early parts of the 20th… …to mix with the rigid world of algebra. The mapping class group offered another algebraic… …Dehn twist automorphisms and proved that the mapping class group is finitely generated by… …these. Nielsen provided a classification of mapping class group elements but supposedly due to…

10 more images…

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APA (6^th Edition):

Pankau, J. C. (2018). On stretch factors of pseudo-Anosov maps. (Thesis). University of California – eScholarship, University of California. Retrieved from http://www.escholarship.org/uc/item/5q48t1cj

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pankau, Joshua Charles. “On stretch factors of pseudo-Anosov maps.” 2018. Thesis, University of California – eScholarship, University of California. Accessed March 08, 2021. http://www.escholarship.org/uc/item/5q48t1cj.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pankau, Joshua Charles. “On stretch factors of pseudo-Anosov maps.” 2018. Web. 08 Mar 2021.

Vancouver:

Pankau JC. On stretch factors of pseudo-Anosov maps. [Internet] [Thesis]. University of California – eScholarship, University of California; 2018. [cited 2021 Mar 08]. Available from: http://www.escholarship.org/uc/item/5q48t1cj.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pankau JC. On stretch factors of pseudo-Anosov maps. [Thesis]. University of California – eScholarship, University of California; 2018. Available from: http://www.escholarship.org/uc/item/5q48t1cj

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. Bavard, Juliette. Dynamique topologique sur les surfaces : gros groupe modulaire & classes de Brouwer : Topological dynamics on surfaces : big class="hilite">mapping class group and Brouwer classes.

Degree: Docteur es, Mathématiques, 2015, Université Pierre et Marie Curie – Paris VI

URL: http://www.theses.fr/2015PA066514

►

On étudie le groupe modulaire G du plan privé d'un ensemble de Cantor et les classes de Brouwer du groupe modulaire du plan privé de… (more)

▼

On étudie le groupe modulaire G du plan privé d'un ensemble de Cantor et les classes de Brouwer du groupe modulaire du plan privé de Z. Ces objets apparaîssent naturellement en dynamique topologique sur les surfaces. Dans le premier chapitre, on s'intéresse au groupe G et à son action sur le graphe des rayons, qui est un analogue déni par Danny Calegari du complexe des courbes pour le plan privé d'un ensemble de Cantor. En particulier, on montre que ce graphe est de diamètre infini et hyperbolique. On utilise ensuite l'action de G sur ce graphe hyperbolique pour exhiber un quasi-morphisme non trivial explicite sur G et pour montrer que le deuxième groupe de cohomologie bornée de G est dedimension infinie. Enfin, on donne un exemple d'un élément hyperbolique de G dont la longueur stable des commutateurs est nulle. Dans le second chapitre, on développe de nouveaux outils pour la théorie de Brouwer homotopique. En particulier, on décrit un ensemble canonique de droites de réduction, l'ensemble des murs, qui sépare le plan en zones de translation maximales et en zones irréductibles. On se restreint ensuite au cas des classes de Brouwer relativement à quatre orbites, et on les décrit explicitement en ajoutant au diagramme de Handel et à l'ensemble des murs un emmêlement, qui est essentiellement une classe d'isotopie de courbes sur le cylindre privé de deux points.

We study the class="hilite">mapping class group G of the complement of a Cantor set in the plane and the Brouwer class="hilite">mapping classes of the class="hilite">mapping class group of the complement of Z in the plane. These objects arise naturally in topological dynamics on surfaces. In the first chapter, we study the group G and its action on the ray graph, which is the analog dened by Danny Calegari of the complex of curves for the complement of a Cantor set in the plane. In particular, we show that this graph has infinite diameter and is hyperbolic. We use the action of G on this graph to find an explicit non trivial quasimorphism on G and to show that this group has infinite dimensional second bounded cohomology. We give an example of a hyperbolic element of G with vanishing stable commutator length. In the second chapter, we give new tools for homotopy Brouwer theory. In particular, we describe a canonical reducing set, the set of "walls", which splits the plane into maximal translation areas and irreducible areas. We then focus on Brouwer class="hilite">mapping classes relatively to four orbits and describe them explicitly by adding to Handel's diagram and to the set of walls a "tangle", which is essentially an isotopy class of simple closed curves in the cylinder minus two points.

Advisors/Committee Members: Le Roux, Frédéric (thesis director).

Subjects/Keywords: Groupe modulaire de surface; Surfaces de type infini; Espace Gromov-Hyperbolique; Quasi-Morphisme; Théorie de Brouwer homotopique; Complexe des courbes; Mapping class group; Homotopy Brouwer theory; 510

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APA (6^th Edition):

Bavard, J. (2015). Dynamique topologique sur les surfaces : gros groupe modulaire & classes de Brouwer : Topological dynamics on surfaces : big mapping class group and Brouwer classes. (Doctoral Dissertation). Université Pierre et Marie Curie – Paris VI. Retrieved from http://www.theses.fr/2015PA066514

Chicago Manual of Style (16^th Edition):

Bavard, Juliette. “Dynamique topologique sur les surfaces : gros groupe modulaire & classes de Brouwer : Topological dynamics on surfaces : big mapping class group and Brouwer classes.” 2015. Doctoral Dissertation, Université Pierre et Marie Curie – Paris VI. Accessed March 08, 2021. http://www.theses.fr/2015PA066514.

MLA Handbook (7^th Edition):

Bavard, Juliette. “Dynamique topologique sur les surfaces : gros groupe modulaire & classes de Brouwer : Topological dynamics on surfaces : big mapping class group and Brouwer classes.” 2015. Web. 08 Mar 2021.

Vancouver:

Bavard J. Dynamique topologique sur les surfaces : gros groupe modulaire & classes de Brouwer : Topological dynamics on surfaces : big mapping class group and Brouwer classes. [Internet] [Doctoral dissertation]. Université Pierre et Marie Curie – Paris VI; 2015. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2015PA066514.

Council of Science Editors:

Bavard J. Dynamique topologique sur les surfaces : gros groupe modulaire & classes de Brouwer : Topological dynamics on surfaces : big mapping class group and Brouwer classes. [Doctoral Dissertation]. Université Pierre et Marie Curie – Paris VI; 2015. Available from: http://www.theses.fr/2015PA066514

21. Tsai, Chia-Yen. Minimal pseudo-Anosov translation lengths on the Teichmuller space.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16103

► This thesis is a study of the asymptotic behavior of minimal pseudo-Anosov translation lengths on the Teichmuller space. For tori with n marked points, we… (more)

Subjects/Keywords: pseudo-Anosov; dilatation; mapping class group; Teichmuller space

…initiated an active research program in the study of the elements of the mapping class group… …introduce some useful tools which are used later in our proofs. 2.1 Mapping class group For more… …detailed discussions of surface homeomorphisms and the mapping class group see [FLP91]… …classes of orientation preserving homeomorphisms f : S → S forms the mapping class group Mod… …about the mapping class group. Its proof can be found in [FLP91]. Theorem 2.1.8…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tsai, C. (2010). Minimal pseudo-Anosov translation lengths on the Teichmuller space. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16103

Chicago Manual of Style (16^th Edition):

Tsai, Chia-Yen. “Minimal pseudo-Anosov translation lengths on the Teichmuller space.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 08, 2021. http://hdl.handle.net/2142/16103.

MLA Handbook (7^th Edition):

Tsai, Chia-Yen. “Minimal pseudo-Anosov translation lengths on the Teichmuller space.” 2010. Web. 08 Mar 2021.

Vancouver:

Tsai C. Minimal pseudo-Anosov translation lengths on the Teichmuller space. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/2142/16103.

Council of Science Editors:

Tsai C. Minimal pseudo-Anosov translation lengths on the Teichmuller space. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16103

22. Ghazouani, Selim. Structures affines complexes sur les surfaces de Riemann : Complex affine structures on Riemann surfaces.

Degree: Docteur es, Mathématiques, 2017, Paris Sciences et Lettres (ComUE)

URL: http://www.theses.fr/2017PSLEE022

►

Cette thèse s'intéresse à des aspects divers des structures affines complexes branchées sur les surfaces de Riemann.Dans une première partie, nous étudions un invariant algébrique… (more)

▼

Cette thèse s'intéresse à des aspects divers des structures affines complexes branchées sur les surfaces de Riemann.Dans une première partie, nous étudions un invariant algébrique de ces structures appelé holonomie, qui est une représentation du groupe fondamental de la surface sous-jacente dans le groupe affine. Nous démontrons un théorème caractérisant les représentations se réalisant comme l'holonomie d'une structure affine.Nous nous intéressons ensuite à la géométrie de certains espaces de modules de telles structures qui viennent naturellement avec une structure hyperbolique complexe. Nous décrivons cette géométrie en terme de dégénérescences de structures affines.Enfin, nous regardons une sous-classe de structures affines dont chaque élément induit une famille de feuilletages sur la surface sous-jacente. Nous relions ces feuilletages à des systèmes dynamiques unidimensionnels appelés échanges d'intervalles affines et nous étudions un cas particulier en détails.

This thesis deals with several aspects of branched, complex affine structures on Riemann surfaces.In a first chapter, we study an algebraic invariant of these structures called holonomy, which is a representation of the fundamental group of the underlying surface into the affine group. We prove a theorem characterising such representations that arise as the holonomy of an affine structure.In a second part, we study certain moduli spaces of affine tori which happen to have an additional complex hyperbolic structure. We analyse the geometry of this structures in terms of degenerations of the underlying affine tori.Finally, we narrow our interest to a subclass of affine structures each element of which inducing a family of foliations on the underlying topological surface. We link these foliations to 1-dimensional dynamical systems called affine interval exchange transformations and study a particular case in details.

Advisors/Committee Members: Deroin, Bertrand (thesis director).

Subjects/Keywords: Surfaces affines; Holonomie; Groupe modulaire; Géométrie hyperbolique complexe; Échanges d'intervalles affines; Affine surfaces; Holonomy; Mapping class group; Complex hyperbolic geometry; Affine interval exchange transformations; 510

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APA (6^th Edition):

Ghazouani, S. (2017). Structures affines complexes sur les surfaces de Riemann : Complex affine structures on Riemann surfaces. (Doctoral Dissertation). Paris Sciences et Lettres (ComUE). Retrieved from http://www.theses.fr/2017PSLEE022

Chicago Manual of Style (16^th Edition):

Ghazouani, Selim. “Structures affines complexes sur les surfaces de Riemann : Complex affine structures on Riemann surfaces.” 2017. Doctoral Dissertation, Paris Sciences et Lettres (ComUE). Accessed March 08, 2021. http://www.theses.fr/2017PSLEE022.

MLA Handbook (7^th Edition):

Ghazouani, Selim. “Structures affines complexes sur les surfaces de Riemann : Complex affine structures on Riemann surfaces.” 2017. Web. 08 Mar 2021.

Vancouver:

Ghazouani S. Structures affines complexes sur les surfaces de Riemann : Complex affine structures on Riemann surfaces. [Internet] [Doctoral dissertation]. Paris Sciences et Lettres (ComUE); 2017. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2017PSLEE022.

Council of Science Editors:

Ghazouani S. Structures affines complexes sur les surfaces de Riemann : Complex affine structures on Riemann surfaces. [Doctoral Dissertation]. Paris Sciences et Lettres (ComUE); 2017. Available from: http://www.theses.fr/2017PSLEE022

23. Martel-Tordjman, Jules. Interprétations homologiques d'invariants quantiques : Homological interprétations of quantum invariants.

Degree: Docteur es, Mathématiques, 2019, Université Toulouse III – Paul Sabatier

URL: http://www.theses.fr/2019TOU30285

►

Cette thèse comporte des interprétations homologiques de certains invariants quantiques, plus particulièrement ceux associés aux groupes de tresses. Le Chapitre 3 étudie des groupes d'homologie… (more)

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Cette thèse comporte des interprétations homologiques de certains invariants quantiques, plus particulièrement ceux associés aux groupes de tresses. Le Chapitre 3 étudie des groupes d'homologie localement finie, relative et à coefficients dans un système local abélien sur des espaces de configurations de points dans le disque épointé. Nous munissons ces complexes d'une action du groupe quantique sl(2) dans une version entière, et nous reconnaissons un produit tensoriel de modules de Verma entiers. Enfin, nous retrouvons une action naturelle du groupe des tresses (par homéomorphisme) sur ces modules homologiques, et nous montrons qu'il s'agit de la représentation obtenue par la R-matrice de la catégorie de modules de sl(2). Les représentations homologiques obtenues sont une généralisation des représentations de Lawrence, donc elles sont fidèles. Elles permettent de retrouver homologiquement plusieurs propriétés de la catégorie de modules sur sl(2). Nous donnons des bases entières de l'homologie (i.e. des bases en tant que module sur un anneau entier de polynômes de Laurent). L'action de sl(2), ainsi que celle du groupe des tresses, respectent cette structure, tout comme l'isomorphisme vers le produit tensoriel de modules de Verma. Ce travail étend le théorème de Kohno (retrouvé via une jolie opération homologique) dans plusieurs directions : • il relie les représentations homologiques à tout le produit tensoriel de modules de Verma (et plus seulement aux vecteurs de plus haut poids) • il inclue une interprétation homologique de l'action de sl(2), dont les définitions sont inspirées par un travail de Felder - Wieczerkowski dans lequel l'aspect homologique restait jusqu'ici conjectural. • il en est une version entière, c'est à dire qu'il préserve la structure d'anneau entier sur les polynômes de Laurent, exhibant ainsi précisément les conditions de généricité précédemment requises par le théorème de Kohno. Ce modèle homologique (pour les représentations quantiques de tresses) est ensuite appliqué aux nœuds vus comme des clôtures de tresses dans le Chapitre 4, et permet d'obtenir une formule des traces (homologiques) pour les polynômes de Jones coloriés, qui s'apparente à une somme pondérée de nombres de Lefschetz abélianisés. Le manuscrit contient également un chapitre (Chapitre 2) d'étude concrète de "petits cas" (car les représentations homologiques sont une famille graduée de représentations). Nous montrons explicitement que les représentations de Gassner du groupe des tresses sont des représentations quantiques, et nous donnons des matrices pour une version colorée des représentations de Bigelow-Krammer-Lawrence - construites au préalable. Nous étudions également le premier niveau de graduation de la représentation du groupe modulaire de la sphère à quatre pointes obtenue via la TQFT non semi-simple (construite par Blanchet - Costantino - Geer - Patureau), nous retrouvons une représentation de nature homologique, ce qui aboutit à la fidélité de cette représentation.

We provide homological interpretations for some…

Advisors/Committee Members: Costantino, Francesco (thesis director).

Subjects/Keywords: Nœuds; Tresses; Espaces de configurations; Groupes modulaires; Homologies; Groupes quantiques; Représentations T0fts; Knots; Braids; Configuration space; Mapping class group; Homologies; Quantum groups; Non semi simples t0fts

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Martel-Tordjman, J. (2019). Interprétations homologiques d'invariants quantiques : Homological interprétations of quantum invariants. (Doctoral Dissertation). Université Toulouse III – Paul Sabatier. Retrieved from http://www.theses.fr/2019TOU30285

Chicago Manual of Style (16^th Edition):

Martel-Tordjman, Jules. “Interprétations homologiques d'invariants quantiques : Homological interprétations of quantum invariants.” 2019. Doctoral Dissertation, Université Toulouse III – Paul Sabatier. Accessed March 08, 2021. http://www.theses.fr/2019TOU30285.

MLA Handbook (7^th Edition):

Martel-Tordjman, Jules. “Interprétations homologiques d'invariants quantiques : Homological interprétations of quantum invariants.” 2019. Web. 08 Mar 2021.

Vancouver:

Martel-Tordjman J. Interprétations homologiques d'invariants quantiques : Homological interprétations of quantum invariants. [Internet] [Doctoral dissertation]. Université Toulouse III – Paul Sabatier; 2019. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2019TOU30285.

Council of Science Editors:

Martel-Tordjman J. Interprétations homologiques d'invariants quantiques : Homological interprétations of quantum invariants. [Doctoral Dissertation]. Université Toulouse III – Paul Sabatier; 2019. Available from: http://www.theses.fr/2019TOU30285

Université de Grenoble

24. Xu, Binbin. L'identité de Pleijel hyperbolique, la métrique de pression et l'extension centrale du groupe modulaire via quantification de Chekhov-Fock : Hyperbolic Pleijel identity, pressure metric and central extension of class="hilite">mapping class group via Chekhov-Fock quantization.

Degree: Docteur es, Mathématiques, 2014, Université de Grenoble

URL: http://www.theses.fr/2014GRENM068

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Cette thèse consiste en trois parties que j'ai faites pendant ces trois ans.La première partie va être constituée de l'étude de la distribution de la… (more)

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Cette thèse consiste en trois parties que j'ai faites pendant ces trois ans.La première partie va être constituée de l'étude de la distribution de la longueur de corde sur le plan hyperbolique. Nous montrons l'identité de Pleijel pour le plan hyperbolique. En utilisant cette identité, nous remontrons l'identité de formule de Crofton et l'inégalité isopérimétrique pour le plan hyperbolique, et puis nous calculons la distribution de la longueur de corde associée à un triangle idéal et celle associée à un quadrilatère idéal. Ensuit, nous montons les résultats analogues pour les surfaces riemannienne simplement connexes avec la courbure constante. La seconde partie va contribuer aux études de la métrique de pression sur l'espace de Teichmüller d'un tore privé d'un disque. En étudiant la dégénération du tore quand la longueur du bord va à l'infini, nous trouvons la relation de cette métrique avec la métrique de pression sur l'espace modulaires des graphes métriques. Nous montrons ensuite que la fonction de l'entropie n'est pas constante sur les feuilles symplectique de l'espace Teichmüller d'une surface à bord.Finalement, la troisième partie concerne la quantification de l'espace de Teichmüller d'une surface avec les piqûres. nous montrons. Dans ce chapitre, nous étudions l'extension centrale du groupe modulaire via la quantification de Chekhov-Fock et calculons sa classe de cohomologie qui est 12 fois la classe de Meyer plus les classes d'Euler associées aux piqûres.

This thesis consists of three parts corresponding to the three subjects that I have studied during the last three years.The first part contains the study of the chord length distribution associated to a compact (or non-compact) domain in the hyperbolic plane. We prove the hyperbolic Pleijel identity. By using this identity, we find new approaches to the Crofton's formula and the isoperimetric inequality, and then compute the chord length distribution associated to an ideal triangle and that associated to an ideal quadrilateral. Then we prove the analogue results for the simply connected Riemannian surface with constant curvature.The second part of this thesis (Chapter 5) consists of the study of the pressuremetric on the Teichmüller space of one-holed torus. By studying the degeneration of the torus when the boundary length goes to infinity, we find the relation of this metric to the pressure metric on the moduli space of metric graphs. Then we study the entropy function and prove that it is not constant on the symplectic leaf of the Teichmüller space of a bordered surface.Finally, the third part concerns the quantization of the Teichmüller space of a punctured surface. In this chapter, we study the central extension of the class="hilite">mapping class group coming from the quantization and compute its cohomology class which is 12 times the Meyer class plus the Euler classes associated to punctures.

Advisors/Committee Members: McShane, Gregory (thesis director), Funar, Louis (thesis director).

Subjects/Keywords: Distribution de longueur de corde; Espace de Techmüller; Espace de modules de graphe; Métrique de pression; Groupe modulaire; Extension centrale; Chord length distribution; Techmüller space; Moduli space of graph; Pressure metric; Mapping class group; Central extension; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Xu, B. (2014). L'identité de Pleijel hyperbolique, la métrique de pression et l'extension centrale du groupe modulaire via quantification de Chekhov-Fock : Hyperbolic Pleijel identity, pressure metric and central extension of mapping class group via Chekhov-Fock quantization. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2014GRENM068

Chicago Manual of Style (16^th Edition):

Xu, Binbin. “L'identité de Pleijel hyperbolique, la métrique de pression et l'extension centrale du groupe modulaire via quantification de Chekhov-Fock : Hyperbolic Pleijel identity, pressure metric and central extension of mapping class group via Chekhov-Fock quantization.” 2014. Doctoral Dissertation, Université de Grenoble. Accessed March 08, 2021. http://www.theses.fr/2014GRENM068.

MLA Handbook (7^th Edition):

Xu, Binbin. “L'identité de Pleijel hyperbolique, la métrique de pression et l'extension centrale du groupe modulaire via quantification de Chekhov-Fock : Hyperbolic Pleijel identity, pressure metric and central extension of mapping class group via Chekhov-Fock quantization.” 2014. Web. 08 Mar 2021.

Vancouver:

Xu B. L'identité de Pleijel hyperbolique, la métrique de pression et l'extension centrale du groupe modulaire via quantification de Chekhov-Fock : Hyperbolic Pleijel identity, pressure metric and central extension of mapping class group via Chekhov-Fock quantization. [Internet] [Doctoral dissertation]. Université de Grenoble; 2014. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2014GRENM068.

Council of Science Editors:

Xu B. L'identité de Pleijel hyperbolique, la métrique de pression et l'extension centrale du groupe modulaire via quantification de Chekhov-Fock : Hyperbolic Pleijel identity, pressure metric and central extension of mapping class group via Chekhov-Fock quantization. [Doctoral Dissertation]. Université de Grenoble; 2014. Available from: http://www.theses.fr/2014GRENM068

25. Vera Arboleda, Anderson Arley. Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois : Johnson-type homomorphisms for surfaces and the universal perturbative invariant of 3-manifolds.

Degree: Docteur es, Mathématiques, 2019, Université de Strasbourg

URL: http://www.theses.fr/2019STRAD009

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Soit Σ une surface compacte connexe orientée avec une seule composante du bord. Notons par M le groupe d'homéotopie de Σ. En considérant l'action de… (more)

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Soit Σ une surface compacte connexe orientée avec une seule composante du bord. Notons par M le groupe d'homéotopie de Σ. En considérant l'action de M sur le groupe fondamental de Σ, il est possible de définir différentes filtrations de M ainsi que des homomorphismes sur chaque terme de ces filtrations. Le but de cette thèse est double. En premier lieu, nous étudions deux filtrations de M : la " filtration de Johnson-Levine " introduite par Levine et la " filtration de Johnson alternative " introduite recemment par Habiro et Massuyeau. Les définitions de ces deux filtrations prennent en compte un corps en anses bordé par la surface. Nous nous référons à ces filtrations comme " filtrations de type Johnson " et les homomorphismes correspondants sont appelés " homomorphismes de type Johnson " par leur analogie avec la filtration de Johnson originale et les homomorphismes de Johnson usuels. Nous donnons une comparaison de la filtration de Johnson avec la filtration de Johnson-Levine au niveau du monoïde des cobordismes d'homologie de Σ. Nous donnons également une comparaison entre la filtration de Johnson alternative, la filtration Johnson-Levine et la filtration de Johnson au niveau du groupe d'homéotopie. Deuxièmement, nous étudions la relation entre les " homomorphismes de type Johnson" et l'extension fonctorielle de l'invariant perturbatif universel des variétés de dimension trois (l'invariant de Le-Murakami-Ohtsuki ou invariant LMO). Cette extension fonctorielle s'appelle le foncteur LMO et il prend ses valeurs dans une catégorie de diagrammes. Nous démontrons que les "homomorphismes de type Johnson " peuvent être lus dans la réduction arborée du foncteur LMO. En particulier, cela fournit une nouvelle grille de lecture de la réduction arborée du foncteur LMO.

Let Σ be a compact oriented surface with one boundary component and let M denote the class="hilite">mapping class group of Σ. By considering the action of M on the fundamental group of Σ it is possible to define different filtrations of M together with some homomorphisms on each term of the filtrations. The aim of this thesis is twofold. First, we study two filtrations of M : the « Johnson-Levine filtration » introduced by Levine and « the alternative Johsnon filtration » introduced recently by Habiro and Massuyeau. The definition of both filtrations involve a handlebody bounded by Σ. We refer to these filtrations as ≪ Johnson-type filtrations » and the corresponding homomorphisms have referred to as « Johnson-type homomorphisms » by their analogy with the original Johnson filtration and the usual Johnson homomorphisms. We provide a comparison of the Johnson filtration with the Johnson-Levine filtration at the level of the monoid of homology cobordisms of Σ. We also provide a comparison of the alternative Johnson filtration with the Johnson-Levine filtration and the Johnson filtration at the level of the class="hilite">mapping class group. Secondly, we study the relationship between the « Johnson-type homomorphisms » and the functorial extension of the universal perturbative invariant of…

Advisors/Committee Members: Massuyeau, Gwénaël (thesis director), Vespa, Christine (thesis director).

Subjects/Keywords: Variétés de dimension trois; Cobordismes d’homologie; Groupe d’homéotopie; Homomorphismes de Johnson; Homomorphismes de Johnson-Levine; Homomorphismes de Johnson alternatifs; Invariant LMO; Foncteur LMO; 3-manifolds; Homology cobordisms; Mapping class group; Johnson homomorphisms; Johnson-Levine homomorphisms; Alternative Johnson homomorphisms; LMO invariant; LMO functor; 512.6; 514.2

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Vera Arboleda, A. A. (2019). Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois : Johnson-type homomorphisms for surfaces and the universal perturbative invariant of 3-manifolds. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2019STRAD009

Chicago Manual of Style (16^th Edition):

Vera Arboleda, Anderson Arley. “Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois : Johnson-type homomorphisms for surfaces and the universal perturbative invariant of 3-manifolds.” 2019. Doctoral Dissertation, Université de Strasbourg. Accessed March 08, 2021. http://www.theses.fr/2019STRAD009.

MLA Handbook (7^th Edition):

Vera Arboleda, Anderson Arley. “Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois : Johnson-type homomorphisms for surfaces and the universal perturbative invariant of 3-manifolds.” 2019. Web. 08 Mar 2021.

Vancouver:

Vera Arboleda AA. Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois : Johnson-type homomorphisms for surfaces and the universal perturbative invariant of 3-manifolds. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2019. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2019STRAD009.

Council of Science Editors:

Vera Arboleda AA. Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois : Johnson-type homomorphisms for surfaces and the universal perturbative invariant of 3-manifolds. [Doctoral Dissertation]. Université de Strasbourg; 2019. Available from: http://www.theses.fr/2019STRAD009

26. Cumplido Cabello, María. Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique : Parabolic subgroups and genericity in Artin-Tits groups of spherical type.

Degree: Docteur es, Mathématiques et leurs interactions, 2018, Rennes 1; Universidad de Sevilla (Espagne)

URL: http://www.theses.fr/2018REN1S022

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Dans la première partie de cette thèse on étudiera la conjecture de généricité: dans le graphe de Cayley du groupe modulaire d'une surface fermée on… (more)

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Dans la première partie de cette thèse on étudiera la conjecture de généricité: dans le graphe de Cayley du groupe modulaire d'une surface fermée on regarde une boule centrée à l'identité et on s'intéresse à la proportion de sommets pseudo-Anosov dans cette boule. La conjecture de généricité affirme que cette proportion doit tendre vers 1 quand le rayon de la boule tend vers l'infini. On montre qu'elle est bornée inférieurement par un nombre strictement positif et on montre des résultats similaires pour une grande classe de sous-groupes du groupe modulaire. On présente aussi des résultats analogues pour des groupes d'Artin-Tits de type sphérique, en sachant que dans ce cas, être pseudo-Anosov est analogue à agir loxodromiquement sur un complexe delta-hyperbolique convenable. Dans la deuxième partie on donne des résultats sur les sous-groupes paraboliques des groupes d'Artin-Tits de type sphérique: le standardisateur minimal d'une courbe dans le disque troué est la tresse minimale positive qui la fait devenir ronde. On construit un algorithme pour le calculer d'une façon géométrique. Ensuite, on généralise le problème pour les groupes d'Artin-Tits de type sphérique. On montre aussi que l'intersection de deux sous-groupes paraboliques est un sous-groupe parabolique et que l'ensemble de sous-groupes paraboliques est un treillis par rapport à l'inclusion. Finalement, on définit le complexe simplicial des sous-groupes paraboliques irréductibles, et on le propose comme l'analogue du complexe de courbes.

In the first part of this thesis we study the genericity conjecture: In the Cayley graph of the class="hilite">mapping class group of a closed surface we look at a ball of large radius centered on the identity vertex, and at the proportion of pseudo-Anosov vertices among the vertices in this ball. The genericity conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero and prove similar results for a large class of subgroups of the class="hilite">mapping class group. We also present analogous results for Artin – Tits groups of spherical type, knowing that in this case being pseudo-Anosov is analogous to being a loxodromically acting element. In the second part we provide results about parabolic subgroups of Artin-Tits groups of spherical type: The minimal standardizer of a curve on a punctured disk is the minimal positive braid that transforms it into a round curve. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin – Tits groups of spherical type. We also show that the intersection of two parabolic subgroups is a parabolic subgroup and that the set of parabolic subgroups forms a lattice with respect to inclusion. Finally, we define the simplicial complex of irreducible parabolic subgroups, and we propose it as the analogue of the curve complex for class="hilite">mapping class groups.

Advisors/Committee Members: Wiest, Bert (thesis director), González-Meneses López, Juan (thesis director).

Subjects/Keywords: Algèbre; Topologie; Groupes d'Artin; Groupe modulaire; Groupe de tresses; Théorie de Garside; Sous-Groupes paraboliques; Actions de groupes; Complexe de courbes; Algebra; Topology; Artin groups; Mapping class groups; Braid theory; Garside theory; Parabolic subgroups; Group actions; Curve complex

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Cumplido Cabello, M. (2018). Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique : Parabolic subgroups and genericity in Artin-Tits groups of spherical type. (Doctoral Dissertation). Rennes 1; Universidad de Sevilla (Espagne). Retrieved from http://www.theses.fr/2018REN1S022

Chicago Manual of Style (16^th Edition):

Cumplido Cabello, María. “Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique : Parabolic subgroups and genericity in Artin-Tits groups of spherical type.” 2018. Doctoral Dissertation, Rennes 1; Universidad de Sevilla (Espagne). Accessed March 08, 2021. http://www.theses.fr/2018REN1S022.

MLA Handbook (7^th Edition):

Cumplido Cabello, María. “Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique : Parabolic subgroups and genericity in Artin-Tits groups of spherical type.” 2018. Web. 08 Mar 2021.

Vancouver:

Cumplido Cabello M. Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique : Parabolic subgroups and genericity in Artin-Tits groups of spherical type. [Internet] [Doctoral dissertation]. Rennes 1; Universidad de Sevilla (Espagne); 2018. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2018REN1S022.

Council of Science Editors:

Cumplido Cabello M. Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique : Parabolic subgroups and genericity in Artin-Tits groups of spherical type. [Doctoral Dissertation]. Rennes 1; Universidad de Sevilla (Espagne); 2018. Available from: http://www.theses.fr/2018REN1S022

27. Hernández Hernández, Jesús. Combinatorial rigidity of complexes of curves and multicurves : Identification and modeling of machining robots' dynamic behavior.

Degree: Docteur es, Mathématiques, 2016, Aix Marseille Université

URL: http://www.theses.fr/2016AIXM4707

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On suppose que S=Sg,n est un surface connexe orientable de type topologique fini, de genre g≥3 et n≥0 épointements. Dans les chapitres 1 et 2… (more)

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On suppose que S=Sg,n est un surface connexe orientable de type topologique fini, de genre g≥3 et n≥0 épointements. Dans les chapitres 1 et 2 on décrit l'ensemble principal d'une surface et prouve que en utilisant expansions rigides itérés, on peut créer suites croissantes d'ensembles finis qui sa réunion est le complexe des courbes de la surface C(S). Dans le 3ème chapitre on introduit l'ensemble rigide X(S) de Aramayona et Leininger et l'utilise pour montrer que la suite des chapitres précédents est eventuellement une suite d'ensembles rigides. On utilise cela pour prouver que si Si=Sgi,ni pour i=1,2 sont surfaces telles que k(S1)≥k(S2) et g1≥3, toute application qui préserve les arêtes de C(S1) dans C(S2) est induite par un homéomorphisme. Ceci est utilisé pour montrer un résultat similaire pour les homomorphismes de sous-groupes de Mod*(S1) dans Mod*(S2). Dans le 4ème chapitre on utilise les résultats précédents pour prouver que l'unique façon d'obtenir une application qui préserve les arêtes et qui est alternante du graphe de Hatcher-Thurston de S1, HT(S1), dans soi de S2, HT(S2) est en utilisant un homéomorphisme de S1 et puis piquer la surface n fois pour obtenir S2. Ceci implique que toute application qui préserve les arêtes et qui est alternante de HT(S) dans soi même et aussi tous les automorphismes de HT(S), sont induits par homéomorphismes. Dans le 5ème chapitre on montre que toute application super-injective du graphe des courbes qui ne sépare pas et courbes extérieures de S1, NO(S1), dans soi de S2, NO(S2), est induite par un homéomorphisme. Finalement, dans les conclusions on discute la signifiance des résultats et les façons possibles d'étendre leur.

Suppose S = Sg,n is an orientable connected surface of finite topological type, with genus g ≥ 3 and n ≥ 0 punctures. In the first two chapters we describe the principal set of a surface, and prove that through iterated rigid expansions we can create an increasing sequence of finite sets whose union in the curve complex of the surface C(S). In the third chapter we introduced Aramayona and Leininger's finite rigid set X(S) and use it to prove that the increasing sequence of the previous two chapters becomes an increasing sequence of finite rigid sets after, at most, the fifth iterated rigid expansion. We use this to prove that given S1 = Sg1,n1 and S2 = Sg2,n2 surfaces such that k(S1) ≥ k(S2) and g1 ≥ 3, any edge-preserving map from C(S1) to C(S2) is induced by a homeomorphism from S1 to S2. This is later used to prove a similar statement using homomorphisms from certain subgroups of Mod*(S1) to Mod*(S2). In the fourth chapter we use the previous results to prove that the only way to obtain an edge-preserving and alternating map from the Hatcher-Thurston graph of S1 = Sg,0, HT(S1), to the Hatcher-Thurston graph of S2 = Sg,n, HT(S2), is using a homeomorphism of S1 and then make n punctures to the surface to obtain S2. As a consequence, any edge-preserving and alternating self-map of HT(S) as well as any automorphism is induced by a homeomorphism. In the…

Advisors/Committee Members: Short, Hamish (thesis director), Aramayona, Javier (thesis director).

Subjects/Keywords: Groupe modulaire; Complexe des courbes; Ensembles rigides; Expansion rigide; Application qui préserve les arêtes; Graphe de Hatcher-Thurston; Applications alternantes; Graphe des courbes qui ne sépare pas et courbes extérieures; Applications super-Injectives; Mapping class group; Curve complex; Rigid sets; Rigid expansions; Edge-Preserving maps; Hatcher-Thurston graph; Alternating maps; Nonseparating and outer curve graph; Superinjective maps

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hernández Hernández, J. (2016). Combinatorial rigidity of complexes of curves and multicurves : Identification and modeling of machining robots' dynamic behavior. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2016AIXM4707

Chicago Manual of Style (16^th Edition):

Hernández Hernández, Jesús. “Combinatorial rigidity of complexes of curves and multicurves : Identification and modeling of machining robots' dynamic behavior.” 2016. Doctoral Dissertation, Aix Marseille Université. Accessed March 08, 2021. http://www.theses.fr/2016AIXM4707.

MLA Handbook (7^th Edition):

Hernández Hernández, Jesús. “Combinatorial rigidity of complexes of curves and multicurves : Identification and modeling of machining robots' dynamic behavior.” 2016. Web. 08 Mar 2021.

Vancouver:

Hernández Hernández J. Combinatorial rigidity of complexes of curves and multicurves : Identification and modeling of machining robots' dynamic behavior. [Internet] [Doctoral dissertation]. Aix Marseille Université 2016. [cited 2021 Mar 08]. Available from: http://www.theses.fr/2016AIXM4707.

Council of Science Editors:

Hernández Hernández J. Combinatorial rigidity of complexes of curves and multicurves : Identification and modeling of machining robots' dynamic behavior. [Doctoral Dissertation]. Aix Marseille Université 2016. Available from: http://www.theses.fr/2016AIXM4707

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