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University of Illinois – Chicago

1.
Simpson, David H.
The Application of Ribbon Hopf Algebras to *Invariants* of 1-1 Tangles.

Degree: 2019, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/23681

► We examine the relation between Ribbon Hopf Algebras and 1-1 Tangles – *knot* diagrams that are cut at a point with the ends pulled apart.…
(more)

Subjects/Keywords: Knot Invariants; Hopf Algebras

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APA (6^{th} Edition):

Simpson, D. H. (2019). The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/23681

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):

Simpson, David H. “The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles.” 2019. Thesis, University of Illinois – Chicago. Accessed July 10, 2020. http://hdl.handle.net/10027/23681.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Simpson, David H. “The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles.” 2019. Web. 10 Jul 2020.

Vancouver:

Simpson DH. The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles. [Internet] [Thesis]. University of Illinois – Chicago; 2019. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/10027/23681.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Simpson DH. The Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles. [Thesis]. University of Illinois – Chicago; 2019. Available from: http://hdl.handle.net/10027/23681

Not specified: Masters Thesis or Doctoral Dissertation

Louisiana State University

2. Hajij, Mustafa. Knots, Skein Theory and q-Series.

Degree: PhD, Applied Mathematics, 2015, Louisiana State University

URL: etd-06222015-181044 ; https://digitalcommons.lsu.edu/gradschool_dissertations/258

► The tail of a sequence {P_{n}(q)} of formal power series in Z[q^{-1}][[q]], if it exists, is the formal power series whose first n coefficients agree…
(more)

Subjects/Keywords: Knot Theory; q-series; Quantum Invariants; Volume Conjecture

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APA (6^{th} Edition):

Hajij, M. (2015). Knots, Skein Theory and q-Series. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-06222015-181044 ; https://digitalcommons.lsu.edu/gradschool_dissertations/258

Chicago Manual of Style (16^{th} Edition):

Hajij, Mustafa. “Knots, Skein Theory and q-Series.” 2015. Doctoral Dissertation, Louisiana State University. Accessed July 10, 2020. etd-06222015-181044 ; https://digitalcommons.lsu.edu/gradschool_dissertations/258.

MLA Handbook (7^{th} Edition):

Hajij, Mustafa. “Knots, Skein Theory and q-Series.” 2015. Web. 10 Jul 2020.

Vancouver:

Hajij M. Knots, Skein Theory and q-Series. [Internet] [Doctoral dissertation]. Louisiana State University; 2015. [cited 2020 Jul 10]. Available from: etd-06222015-181044 ; https://digitalcommons.lsu.edu/gradschool_dissertations/258.

Council of Science Editors:

Hajij M. Knots, Skein Theory and q-Series. [Doctoral Dissertation]. Louisiana State University; 2015. Available from: etd-06222015-181044 ; https://digitalcommons.lsu.edu/gradschool_dissertations/258

Princeton University

3.
Racz, Bela Andras.
Geometry of (1,1)-Knots and *Knot* Floer Homology
.

Degree: PhD, 2015, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01ft848s85j

► We apply the technique of Heegaard Floer Homology to (1,1)-knots (1-bridge knots on the torus) to determine all (1,1)-knots of crossing number up to 12.…
(more)

Subjects/Keywords: (1,1)-knots; grid diagrams; Heegaard Floer homology; knot invariants

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APA (6^{th} Edition):

Racz, B. A. (2015). Geometry of (1,1)-Knots and Knot Floer Homology . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01ft848s85j

Chicago Manual of Style (16^{th} Edition):

Racz, Bela Andras. “Geometry of (1,1)-Knots and Knot Floer Homology .” 2015. Doctoral Dissertation, Princeton University. Accessed July 10, 2020. http://arks.princeton.edu/ark:/88435/dsp01ft848s85j.

MLA Handbook (7^{th} Edition):

Racz, Bela Andras. “Geometry of (1,1)-Knots and Knot Floer Homology .” 2015. Web. 10 Jul 2020.

Vancouver:

Racz BA. Geometry of (1,1)-Knots and Knot Floer Homology . [Internet] [Doctoral dissertation]. Princeton University; 2015. [cited 2020 Jul 10]. Available from: http://arks.princeton.edu/ark:/88435/dsp01ft848s85j.

Council of Science Editors:

Racz BA. Geometry of (1,1)-Knots and Knot Floer Homology . [Doctoral Dissertation]. Princeton University; 2015. Available from: http://arks.princeton.edu/ark:/88435/dsp01ft848s85j

Princeton University

4. Mikhaylov, Victor. Aspects Of Supergroup Chern-Simons Theories .

Degree: PhD, 2015, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01zw12z768m

► The three-dimensional Chern-Simons gauge theory is a topological quantum field theory, whose correlation functions give metric-independent *invariants* of knots and three-manifolds. In this thesis, we…
(more)

Subjects/Keywords: Chern-Simons Theory; Knot Invariants; Lie Supergroups; Topological Quantum Field Theory

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APA (6^{th} Edition):

Mikhaylov, V. (2015). Aspects Of Supergroup Chern-Simons Theories . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01zw12z768m

Chicago Manual of Style (16^{th} Edition):

Mikhaylov, Victor. “Aspects Of Supergroup Chern-Simons Theories .” 2015. Doctoral Dissertation, Princeton University. Accessed July 10, 2020. http://arks.princeton.edu/ark:/88435/dsp01zw12z768m.

MLA Handbook (7^{th} Edition):

Mikhaylov, Victor. “Aspects Of Supergroup Chern-Simons Theories .” 2015. Web. 10 Jul 2020.

Vancouver:

Mikhaylov V. Aspects Of Supergroup Chern-Simons Theories . [Internet] [Doctoral dissertation]. Princeton University; 2015. [cited 2020 Jul 10]. Available from: http://arks.princeton.edu/ark:/88435/dsp01zw12z768m.

Council of Science Editors:

Mikhaylov V. Aspects Of Supergroup Chern-Simons Theories . [Doctoral Dissertation]. Princeton University; 2015. Available from: http://arks.princeton.edu/ark:/88435/dsp01zw12z768m

Rice University

5.
Davis, Christopher.
First Order Signatures and *Knot* Concordance.

Degree: PhD, Natural Sciences, 2012, Rice University

URL: http://hdl.handle.net/1911/64621

► *Invariants* of knots coming from twisted signatures have played a central role in the study of *knot* concordance. Unfortunately, except in the simplest of cases,…
(more)

Subjects/Keywords: Knot concordance; L2 Homology; Twisted signatures; Rho invariants

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APA (6^{th} Edition):

Davis, C. (2012). First Order Signatures and Knot Concordance. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/64621

Chicago Manual of Style (16^{th} Edition):

Davis, Christopher. “First Order Signatures and Knot Concordance.” 2012. Doctoral Dissertation, Rice University. Accessed July 10, 2020. http://hdl.handle.net/1911/64621.

MLA Handbook (7^{th} Edition):

Davis, Christopher. “First Order Signatures and Knot Concordance.” 2012. Web. 10 Jul 2020.

Vancouver:

Davis C. First Order Signatures and Knot Concordance. [Internet] [Doctoral dissertation]. Rice University; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1911/64621.

Council of Science Editors:

Davis C. First Order Signatures and Knot Concordance. [Doctoral Dissertation]. Rice University; 2012. Available from: http://hdl.handle.net/1911/64621

University of Tennessee – Knoxville

6. Manathunga, Vajira Asanka. The Conway Polynomial and Amphicheiral Knots.

Degree: 2016, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_graddiss/3721

► The Conant's conjecture [7] which has foundation on the Conway polynomial and Vassiliev *invariants* is the main theme of this research. The Conant's conjecture claim…
(more)

Subjects/Keywords: Knot theory; Amphicheiral knots; Conway polynomial; Vassiliev invariants; Geometry and Topology

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APA (6^{th} Edition):

Manathunga, V. A. (2016). The Conway Polynomial and Amphicheiral Knots. (Doctoral Dissertation). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_graddiss/3721

Chicago Manual of Style (16^{th} Edition):

Manathunga, Vajira Asanka. “The Conway Polynomial and Amphicheiral Knots.” 2016. Doctoral Dissertation, University of Tennessee – Knoxville. Accessed July 10, 2020. https://trace.tennessee.edu/utk_graddiss/3721.

MLA Handbook (7^{th} Edition):

Manathunga, Vajira Asanka. “The Conway Polynomial and Amphicheiral Knots.” 2016. Web. 10 Jul 2020.

Vancouver:

Manathunga VA. The Conway Polynomial and Amphicheiral Knots. [Internet] [Doctoral dissertation]. University of Tennessee – Knoxville; 2016. [cited 2020 Jul 10]. Available from: https://trace.tennessee.edu/utk_graddiss/3721.

Council of Science Editors:

Manathunga VA. The Conway Polynomial and Amphicheiral Knots. [Doctoral Dissertation]. University of Tennessee – Knoxville; 2016. Available from: https://trace.tennessee.edu/utk_graddiss/3721

University of Iowa

7.
Yildirim, Tuna.
Topologically massive Yang-Mills theory and link * invariants*.

Degree: PhD, Physics, 2014, University of Iowa

URL: https://ir.uiowa.edu/etd/1519

► In this thesis, topologically massive Yang-Mills theory is studied in the framework of geometric quantization. This theory has a mass gap that is proportional…
(more)

Subjects/Keywords: publicabstract; Chern Simons; Geometric Quantization; Knot Theory; Link Invariants; Topological Field Theory; Yang Mills; Physics

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APA (6^{th} Edition):

Yildirim, T. (2014). Topologically massive Yang-Mills theory and link invariants. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/1519

Chicago Manual of Style (16^{th} Edition):

Yildirim, Tuna. “Topologically massive Yang-Mills theory and link invariants.” 2014. Doctoral Dissertation, University of Iowa. Accessed July 10, 2020. https://ir.uiowa.edu/etd/1519.

MLA Handbook (7^{th} Edition):

Yildirim, Tuna. “Topologically massive Yang-Mills theory and link invariants.” 2014. Web. 10 Jul 2020.

Vancouver:

Yildirim T. Topologically massive Yang-Mills theory and link invariants. [Internet] [Doctoral dissertation]. University of Iowa; 2014. [cited 2020 Jul 10]. Available from: https://ir.uiowa.edu/etd/1519.

Council of Science Editors:

Yildirim T. Topologically massive Yang-Mills theory and link invariants. [Doctoral Dissertation]. University of Iowa; 2014. Available from: https://ir.uiowa.edu/etd/1519

8.
Kohli, Ben-Michael.
Les *invariants* de Links-Gould comme généralisations du polynôme d’Alexander : The Links-Gould *invariants* as generalizations of the Alexander polynomial.

Degree: Docteur es, Mathématiques, 2016, Université de Bourgogne

URL: http://www.theses.fr/2016DIJOS062

►

On s’intéresse dans cette thèse aux rapports qui existent entre deux *invariants* d’entrelacs. D’une part l’invariant d’Alexander ∆ qui est l’invariant de nœuds le plus…
(more)

Subjects/Keywords: Nœud; Entrelacs; Polynôme d’Alexander; Invariants de Links-Gould; Algèbre de Hopf; R-matrice; Genre; Nœud fibré; Knot; Link; Alexander polynomial; Links-Gould invariants; Hopf algebra; R- matrix; Genus; Fiberedness; 515

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APA (6^{th} Edition):

Kohli, B. (2016). Les invariants de Links-Gould comme généralisations du polynôme d’Alexander : The Links-Gould invariants as generalizations of the Alexander polynomial. (Doctoral Dissertation). Université de Bourgogne. Retrieved from http://www.theses.fr/2016DIJOS062

Chicago Manual of Style (16^{th} Edition):

Kohli, Ben-Michael. “Les invariants de Links-Gould comme généralisations du polynôme d’Alexander : The Links-Gould invariants as generalizations of the Alexander polynomial.” 2016. Doctoral Dissertation, Université de Bourgogne. Accessed July 10, 2020. http://www.theses.fr/2016DIJOS062.

MLA Handbook (7^{th} Edition):

Kohli, Ben-Michael. “Les invariants de Links-Gould comme généralisations du polynôme d’Alexander : The Links-Gould invariants as generalizations of the Alexander polynomial.” 2016. Web. 10 Jul 2020.

Vancouver:

Kohli B. Les invariants de Links-Gould comme généralisations du polynôme d’Alexander : The Links-Gould invariants as generalizations of the Alexander polynomial. [Internet] [Doctoral dissertation]. Université de Bourgogne; 2016. [cited 2020 Jul 10]. Available from: http://www.theses.fr/2016DIJOS062.

Council of Science Editors:

Kohli B. Les invariants de Links-Gould comme généralisations du polynôme d’Alexander : The Links-Gould invariants as generalizations of the Alexander polynomial. [Doctoral Dissertation]. Université de Bourgogne; 2016. Available from: http://www.theses.fr/2016DIJOS062

9. Corbineau, Kévin. Sur une anomalie du développement perturbatif de la théorie de Chern-Simons : On an anomaly of the perturbative expansion of Chern-Simons theory.

Degree: Docteur es, Mathématiques, 2016, Université Grenoble Alpes (ComUE)

URL: http://www.theses.fr/2016GREAM038

►

Maxim Kontsevich a défini un invariant Z des sphères d'homologie rationnelle orientées de dimension 3 en 1992, en poursuivant l'étude initiée par Edward Witten du… (more)

Subjects/Keywords: Espaces de configurations; Sphère d'homologie rationnelle; Invariants de noeud; Anomalie; Développement perturbatif de la théorie de Chern-Simons; Configuration space; Rational homology sphere; Knot invariants; Anomaly; Perturbative expansion of Chern-Simons theory; 510

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APA (6^{th} Edition):

Corbineau, K. (2016). Sur une anomalie du développement perturbatif de la théorie de Chern-Simons : On an anomaly of the perturbative expansion of Chern-Simons theory. (Doctoral Dissertation). Université Grenoble Alpes (ComUE). Retrieved from http://www.theses.fr/2016GREAM038

Chicago Manual of Style (16^{th} Edition):

Corbineau, Kévin. “Sur une anomalie du développement perturbatif de la théorie de Chern-Simons : On an anomaly of the perturbative expansion of Chern-Simons theory.” 2016. Doctoral Dissertation, Université Grenoble Alpes (ComUE). Accessed July 10, 2020. http://www.theses.fr/2016GREAM038.

MLA Handbook (7^{th} Edition):

Corbineau, Kévin. “Sur une anomalie du développement perturbatif de la théorie de Chern-Simons : On an anomaly of the perturbative expansion of Chern-Simons theory.” 2016. Web. 10 Jul 2020.

Vancouver:

Corbineau K. Sur une anomalie du développement perturbatif de la théorie de Chern-Simons : On an anomaly of the perturbative expansion of Chern-Simons theory. [Internet] [Doctoral dissertation]. Université Grenoble Alpes (ComUE); 2016. [cited 2020 Jul 10]. Available from: http://www.theses.fr/2016GREAM038.

Council of Science Editors:

Corbineau K. Sur une anomalie du développement perturbatif de la théorie de Chern-Simons : On an anomaly of the perturbative expansion of Chern-Simons theory. [Doctoral Dissertation]. Université Grenoble Alpes (ComUE); 2016. Available from: http://www.theses.fr/2016GREAM038

10. Chu, Karene Kayin. Flat Virtual Pure Tangles.

Degree: 2012, University of Toronto

URL: http://hdl.handle.net/1807/33962

►

Virtual *knot* theory, introduced by Kauffman, is a generalization of classical *knot* theory of interest because its finite-type invariant theory is potentially a topological interpretation…
(more)

Subjects/Keywords: virtual knot; flat virtual knot; finite-type invariants; R-matrix; quantum invariant; immersed curves; 0405

…knots, where “long” simply refers to the
skeleton of the *knot* being a long line, and the… …skeleton” is the union of lines and/or
circles obtained from tracing the *knot* diagram along the… …a canonical representative for each equivalent class
of descending virtual long *knot*… …long *knot* diagram whose
skeleton strand has a point before which it is the over strand in any… …virtual long *knot*.
There is a point on the skeleton before which it is the over strand in all…

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APA (6^{th} Edition):

Chu, K. K. (2012). Flat Virtual Pure Tangles. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/33962

Chicago Manual of Style (16^{th} Edition):

Chu, Karene Kayin. “Flat Virtual Pure Tangles.” 2012. Doctoral Dissertation, University of Toronto. Accessed July 10, 2020. http://hdl.handle.net/1807/33962.

MLA Handbook (7^{th} Edition):

Chu, Karene Kayin. “Flat Virtual Pure Tangles.” 2012. Web. 10 Jul 2020.

Vancouver:

Chu KK. Flat Virtual Pure Tangles. [Internet] [Doctoral dissertation]. University of Toronto; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1807/33962.

Council of Science Editors:

Chu KK. Flat Virtual Pure Tangles. [Doctoral Dissertation]. University of Toronto; 2012. Available from: http://hdl.handle.net/1807/33962

California State University – San Bernardino

11.
Wheeler, Russell Clark.
Using symbolic dynamical systems: A search for *knot* * invariants*.

Degree: MAin Mathematics, Mathematics, 1998, California State University – San Bernardino

URL: https://scholarworks.lib.csusb.edu/etd-project/3033

Subjects/Keywords: Knot theory; Three-manifolds (Topology); Invariants; Quantum field theory; Mathematical physics; Braid theory; Braid theory; Invariants; Knot theory; Mathematical physics; Quantum field theory; Three-manifolds (Topology); Geometry and Topology

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APA (6^{th} Edition):

Wheeler, R. C. (1998). Using symbolic dynamical systems: A search for knot invariants. (Thesis). California State University – San Bernardino. Retrieved from https://scholarworks.lib.csusb.edu/etd-project/3033

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Wheeler, Russell Clark. “Using symbolic dynamical systems: A search for knot invariants.” 1998. Thesis, California State University – San Bernardino. Accessed July 10, 2020. https://scholarworks.lib.csusb.edu/etd-project/3033.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Wheeler, Russell Clark. “Using symbolic dynamical systems: A search for knot invariants.” 1998. Web. 10 Jul 2020.

Vancouver:

Wheeler RC. Using symbolic dynamical systems: A search for knot invariants. [Internet] [Thesis]. California State University – San Bernardino; 1998. [cited 2020 Jul 10]. Available from: https://scholarworks.lib.csusb.edu/etd-project/3033.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wheeler RC. Using symbolic dynamical systems: A search for knot invariants. [Thesis]. California State University – San Bernardino; 1998. Available from: https://scholarworks.lib.csusb.edu/etd-project/3033

Not specified: Masters Thesis or Doctoral Dissertation

California State University – San Bernardino

12.
Wheeler, Russell Clark.
Using symbolic dynamical systems: A search for *knot* * invariants*.

Degree: MAin Mathematics, Mathematics, 1998, California State University – San Bernardino

URL: https://scholarworks.lib.csusb.edu/etd-project/3165

Subjects/Keywords: Knot theory; Three-manifolds (Topology); Invariants; Quantum field theory; Mathematical physics; Braid theory; Braid theory; Invariants; Knot theory; Mathematical physics; Quantum field theory; Three-manifolds (Topology); Geometry and Topology

Record Details Similar Records

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APA (6^{th} Edition):

Wheeler, R. C. (1998). Using symbolic dynamical systems: A search for knot invariants. (Thesis). California State University – San Bernardino. Retrieved from https://scholarworks.lib.csusb.edu/etd-project/3165

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Wheeler, Russell Clark. “Using symbolic dynamical systems: A search for knot invariants.” 1998. Thesis, California State University – San Bernardino. Accessed July 10, 2020. https://scholarworks.lib.csusb.edu/etd-project/3165.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Wheeler, Russell Clark. “Using symbolic dynamical systems: A search for knot invariants.” 1998. Web. 10 Jul 2020.

Vancouver:

Wheeler RC. Using symbolic dynamical systems: A search for knot invariants. [Internet] [Thesis]. California State University – San Bernardino; 1998. [cited 2020 Jul 10]. Available from: https://scholarworks.lib.csusb.edu/etd-project/3165.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wheeler RC. Using symbolic dynamical systems: A search for knot invariants. [Thesis]. California State University – San Bernardino; 1998. Available from: https://scholarworks.lib.csusb.edu/etd-project/3165

Not specified: Masters Thesis or Doctoral Dissertation

13. Martin, Taylor. Lower order solvability of links.

Degree: PhD, Natural Sciences, 2013, Rice University

URL: http://hdl.handle.net/1911/71998

► The n-solvable filtration of the link concordance group, defined by Cochran, Orr, and Teichner in 2003, is a tool for studying smooth *knot* and link…
(more)

Subjects/Keywords: Knot theory; Link concordance; N-solvable filtration; Band-pass equivalence; Milnor's invariants

…oriented
circles into the three-sphere. A *knot* is a link with only one component. Two links
are… …form an abelian
group under an operation called connected sum, called the *knot* concordance… …is the equivalence
class of the trivial *knot*. Any *knot* in this class is called slice. The… …*knot* concordance
group has been well-studied since its introduction, but its structure is… …concordance group, C m , where m is
the number of link components; when m = 1, this is the *knot*…

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APA (6^{th} Edition):

Martin, T. (2013). Lower order solvability of links. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/71998

Chicago Manual of Style (16^{th} Edition):

Martin, Taylor. “Lower order solvability of links.” 2013. Doctoral Dissertation, Rice University. Accessed July 10, 2020. http://hdl.handle.net/1911/71998.

MLA Handbook (7^{th} Edition):

Martin, Taylor. “Lower order solvability of links.” 2013. Web. 10 Jul 2020.

Vancouver:

Martin T. Lower order solvability of links. [Internet] [Doctoral dissertation]. Rice University; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1911/71998.

Council of Science Editors:

Martin T. Lower order solvability of links. [Doctoral Dissertation]. Rice University; 2013. Available from: http://hdl.handle.net/1911/71998

14. Kuzbary, Miriam. Link Concordance and Groups.

Degree: PhD, Natural Sciences, 2019, Rice University

URL: http://hdl.handle.net/1911/105956

► This work concerns the study of link concordance using groups, both extracting concordance data from group theoretic *invariants* and determining the properties of group structures…
(more)

Subjects/Keywords: low dimensional topology; geometric topology; link concordance; knot concordance; group theory; nilpotent groups; Milnor's invariants; Heegaard Floer homology

…the connected sum of two knots. . . . . . . . .
The so-called Borromean *knot* B ⊂ #2 S 2 × S… …nullhomologous *knot* in S 1 × S 2 . . . . . . . . . . . . . . . .
J3 ⊂ #2 S 2 × S 1 and J4 ⊂ #3 S 2 × S… …to
better understanding the world around us.
It is perhaps a surprising fact that *knot*… …theory provides a useful tool for studying
3- and 4-dimensional spaces. A *knot* is a smooth… …other as in Figure 1.
z
z
y
x
y
x
(a) A *knot*.
(b) A 2-component…

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APA (6^{th} Edition):

Kuzbary, M. (2019). Link Concordance and Groups. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/105956

Chicago Manual of Style (16^{th} Edition):

Kuzbary, Miriam. “Link Concordance and Groups.” 2019. Doctoral Dissertation, Rice University. Accessed July 10, 2020. http://hdl.handle.net/1911/105956.

MLA Handbook (7^{th} Edition):

Kuzbary, Miriam. “Link Concordance and Groups.” 2019. Web. 10 Jul 2020.

Vancouver:

Kuzbary M. Link Concordance and Groups. [Internet] [Doctoral dissertation]. Rice University; 2019. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1911/105956.

Council of Science Editors:

Kuzbary M. Link Concordance and Groups. [Doctoral Dissertation]. Rice University; 2019. Available from: http://hdl.handle.net/1911/105956

15. Tran, Anh Tuan. The volume conjecture, the aj conjectures and skein modules.

Degree: PhD, Mathematics, 2012, Georgia Tech

URL: http://hdl.handle.net/1853/44811

► This dissertation studies quantum *invariants* of knots and links, particularly the colored Jones polynomials, and their relationships with classical *invariants* like the hyperbolic volume and…
(more)

Subjects/Keywords: Volume conjecture; AJ conjecture; Skein module; Colored Jones polynomial; A-polynomial; Knot theory; Symmetry (Mathematics); Invariants; Invariant manifolds; Hyperbolic spaces

…SUMMARY
This dissertation studies quantum *invariants* of knots and links, particularly… …the
colored Jones polynomials, and their relationships with classical *invariants* like the… …conjecture for (m, 2)-cables of the figure 8 *knot*, when m is odd. For (m, 2)… …when the volume conjecture for cables of the figure 8 *knot* is false if one considers all
the… …relations of the colored Jones polynomials and the A-polynomial of a *knot*,
using skein theory. We…

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APA (6^{th} Edition):

Tran, A. T. (2012). The volume conjecture, the aj conjectures and skein modules. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/44811

Chicago Manual of Style (16^{th} Edition):

Tran, Anh Tuan. “The volume conjecture, the aj conjectures and skein modules.” 2012. Doctoral Dissertation, Georgia Tech. Accessed July 10, 2020. http://hdl.handle.net/1853/44811.

MLA Handbook (7^{th} Edition):

Tran, Anh Tuan. “The volume conjecture, the aj conjectures and skein modules.” 2012. Web. 10 Jul 2020.

Vancouver:

Tran AT. The volume conjecture, the aj conjectures and skein modules. [Internet] [Doctoral dissertation]. Georgia Tech; 2012. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/1853/44811.

Council of Science Editors:

Tran AT. The volume conjecture, the aj conjectures and skein modules. [Doctoral Dissertation]. Georgia Tech; 2012. Available from: http://hdl.handle.net/1853/44811