subject:( KK theory)

1. Van Den Dungen, Koen. Lorentzian geometry and physics in Kasparov's theory .

Degree: 2015, Australian National University

► We study two geometric themes, Lorentzian geometry and gauge theory, from the perspective of Connes’ noncommutative geometry and (the unbounded version of) Kasparov’s KK-theory. Lorentzian… (more)

▼ We study two geometric themes, Lorentzian geometry and gauge theory, from the perspective of Connes’ noncommutative geometry and (the unbounded version of) Kasparov’s KK-theory. Lorentzian geometry is the mathematical framework underlying Einstein’s description of gravity. The geometric formulation of a gauge theory (in terms of principal bundles) offers a classical description for the interactions between particles. The underlying motivation is the hope that this noncommutative approach may lead to a unified description of gauge theories coupled with gravity on a Lorentzian manifold. The main objects in noncommutative geometry are spectral triples, which encompass and generalise Riemannian spin manifolds. A spectral triple defines a class in K-homology, via which one can access the topology of the (noncommutative) manifold. In this thesis we present two possible definitions for ‘Lorentian spectral triples’, which offer noncommutative generalisations of Lorentzian manifolds as well. We will prove that both definitions preserve the link with analytic K-homology. We will describe under which conditions Lorentzian (or pseudo- Riemannian) manifolds satisfy these definitions. Another main example is the harmonic oscillator, which in particular shows that our framework allows to deal with more than just metrics of indefinite signature. In the context of noncommutative geometry, the description of a gauge theory can be obtained from so-called almost-commutative manifolds. While the usual approach yields by default a topologically trivial gauge theory (in the sense that the corresponding principal fibre bundle is globally trivial), we show in this thesis that the framework can be adapted, using the internal unbounded Kasparov product, to allow for globally non-trivial gauge theories as well. Finally, we combine the two themes of Lorentzian geometry and gauge theory, and we define Krein spectral triples, which generalise spectral triples from Hilbert spaces to Krein spaces. We use this definition to construct almost-commutative Lorentzian manifolds. Furthermore, we propose a Lorentzian alternative for the fermionic action, which allows to derive (the fermionic part of) the Lagrangian of a gauge theory. We show that our alternative action recovers exactly the correct physical Lagrangian.

Subjects/Keywords: Connes' noncommutative geometry; Kasparov's KK-theory; Lorentzian

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APA (6^th Edition):

Van Den Dungen, K. (2015). Lorentzian geometry and physics in Kasparov's theory . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/15240

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):

Van Den Dungen, Koen. “Lorentzian geometry and physics in Kasparov's theory .” 2015. Thesis, Australian National University. Accessed January 28, 2021. http://hdl.handle.net/1885/15240.

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

MLA Handbook (7^th Edition):

Van Den Dungen, Koen. “Lorentzian geometry and physics in Kasparov's theory .” 2015. Web. 28 Jan 2021.

Vancouver:

Van Den Dungen K. Lorentzian geometry and physics in Kasparov's theory . [Internet] [Thesis]. Australian National University; 2015. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/1885/15240.

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

Council of Science Editors:

Van Den Dungen K. Lorentzian geometry and physics in Kasparov's theory . [Thesis]. Australian National University; 2015. Available from: http://hdl.handle.net/1885/15240

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

Australian National University

2. Forsyth, Iain Graham. Boundaries and equivariant products in unbounded Kasparov theory .

Degree: 2016, Australian National University

URL: http://hdl.handle.net/1885/101227

► The thesis explores two distinct areas of noncommutative geometry: factorisation and boundaries. Both of these topics are concerned with cycles in Kasparov’s KK-theory which are… (more)

Subjects/Keywords: KK-theory; spectral triple; Kasparov product

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APA (6^th Edition):

Forsyth, I. G. (2016). Boundaries and equivariant products in unbounded Kasparov theory . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/101227

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):

Forsyth, Iain Graham. “Boundaries and equivariant products in unbounded Kasparov theory .” 2016. Thesis, Australian National University. Accessed January 28, 2021. http://hdl.handle.net/1885/101227.

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

MLA Handbook (7^th Edition):

Forsyth, Iain Graham. “Boundaries and equivariant products in unbounded Kasparov theory .” 2016. Web. 28 Jan 2021.

Vancouver:

Forsyth IG. Boundaries and equivariant products in unbounded Kasparov theory . [Internet] [Thesis]. Australian National University; 2016. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/1885/101227.

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

Council of Science Editors:

Forsyth IG. Boundaries and equivariant products in unbounded Kasparov theory . [Thesis]. Australian National University; 2016. Available from: http://hdl.handle.net/1885/101227

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

Cornell University

3. Leung, Ho Hon. K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory.

Degree: PhD, Mathematics, 2011, Cornell University

URL: http://hdl.handle.net/1813/29318

► This thesis consists of two chapters. In the first chapter, we compute the K theory of weight varieties by using techniques in Hamiltonian geometry. In… (more)

Subjects/Keywords: Symplectic Geometry; Operator Algebras; Divided difference operators; KK-theory

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APA (6^th Edition):

Leung, H. H. (2011). K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/29318

Chicago Manual of Style (16^th Edition):

Leung, Ho Hon. “K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory.” 2011. Doctoral Dissertation, Cornell University. Accessed January 28, 2021. http://hdl.handle.net/1813/29318.

MLA Handbook (7^th Edition):

Leung, Ho Hon. “K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory.” 2011. Web. 28 Jan 2021.

Vancouver:

Leung HH. K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory. [Internet] [Doctoral dissertation]. Cornell University; 2011. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/1813/29318.

Council of Science Editors:

Leung HH. K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory. [Doctoral Dissertation]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/29318

Penn State University

4. Raven, Jeff. AN EQUIVARIANT BIVARIANT CHERN CHARACTER.

Degree: 2008, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/6464

► Using notions from homological algebra and sheaf theory Baum and Schneider defined a bivariant equivariant cohomology theory which shares many of the properties of equivariant… (more)

Subjects/Keywords: equivariant kk-theory; chern characters

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APA (6^th Edition):

Raven, J. (2008). AN EQUIVARIANT BIVARIANT CHERN CHARACTER. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/6464

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):

Raven, Jeff. “AN EQUIVARIANT BIVARIANT CHERN CHARACTER.” 2008. Thesis, Penn State University. Accessed January 28, 2021. https://submit-etda.libraries.psu.edu/catalog/6464.

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

MLA Handbook (7^th Edition):

Raven, Jeff. “AN EQUIVARIANT BIVARIANT CHERN CHARACTER.” 2008. Web. 28 Jan 2021.

Vancouver:

Raven J. AN EQUIVARIANT BIVARIANT CHERN CHARACTER. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Jan 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/6464.

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

Council of Science Editors:

Raven J. AN EQUIVARIANT BIVARIANT CHERN CHARACTER. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/6464

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

Australian National University

5. Bourne, Christopher. Topological states of matter and noncommutative geometry .

Degree: 2015, Australian National University

URL: http://hdl.handle.net/1885/16960

► This thesis examines topological states of matter from the perspective of noncommutative geometry and KK-theory. Examples of such topological states of matter include the quantum… (more)

Subjects/Keywords: Noncommutative geometry; KK-theory; topological insulators; topological phases

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APA (6^th Edition):

Bourne, C. (2015). Topological states of matter and noncommutative geometry . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/16960

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):

Bourne, Christopher. “Topological states of matter and noncommutative geometry .” 2015. Thesis, Australian National University. Accessed January 28, 2021. http://hdl.handle.net/1885/16960.

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

MLA Handbook (7^th Edition):

Bourne, Christopher. “Topological states of matter and noncommutative geometry .” 2015. Web. 28 Jan 2021.

Vancouver:

Bourne C. Topological states of matter and noncommutative geometry . [Internet] [Thesis]. Australian National University; 2015. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/1885/16960.

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

Council of Science Editors:

Bourne C. Topological states of matter and noncommutative geometry . [Thesis]. Australian National University; 2015. Available from: http://hdl.handle.net/1885/16960

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

Penn State University

6. Nishikawa, Shintaro. Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces.

Degree: 2020, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/17440sxn28

► The Baum–Connes conjecture is one of the most important open problems in noncommutative geometry. In the 1980’s, Gennadi Kasparov introduced his equivariant KK-theory and brought… (more)

Subjects/Keywords: the Baum-Connes conjecture; KK-theory; K-theory; C*-algebras; CAT(0)-cubical space

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APA (6^th Edition):

Nishikawa, S. (2020). Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/17440sxn28

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):

Nishikawa, Shintaro. “Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces.” 2020. Thesis, Penn State University. Accessed January 28, 2021. https://submit-etda.libraries.psu.edu/catalog/17440sxn28.

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

MLA Handbook (7^th Edition):

Nishikawa, Shintaro. “Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces.” 2020. Web. 28 Jan 2021.

Vancouver:

Nishikawa S. Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces. [Internet] [Thesis]. Penn State University; 2020. [cited 2021 Jan 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/17440sxn28.

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

Council of Science Editors:

Nishikawa S. Direct splitting method for the Baum-Connes conjecture and groups acting on CAT(0)-cubical spaces. [Thesis]. Penn State University; 2020. Available from: https://submit-etda.libraries.psu.edu/catalog/17440sxn28

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

Virginia Tech

7. Ordonez-Delgado, Bartleby. An Embedded Toeplitz Problem.

Degree: PhD, Mathematics, 2010, Virginia Tech

URL: http://hdl.handle.net/10919/29007

► In this work we investigate multi-variable Toeplitz operators and their relationship with KK-theory in order to apply this relationship to define and analyze embedded Toeplitz… (more)

Subjects/Keywords: Index Theory; KK-Theory; Toeplitz operators

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APA (6^th Edition):

Ordonez-Delgado, B. (2010). An Embedded Toeplitz Problem. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/29007

Chicago Manual of Style (16^th Edition):

Ordonez-Delgado, Bartleby. “An Embedded Toeplitz Problem.” 2010. Doctoral Dissertation, Virginia Tech. Accessed January 28, 2021. http://hdl.handle.net/10919/29007.

MLA Handbook (7^th Edition):

Ordonez-Delgado, Bartleby. “An Embedded Toeplitz Problem.” 2010. Web. 28 Jan 2021.

Vancouver:

Ordonez-Delgado B. An Embedded Toeplitz Problem. [Internet] [Doctoral dissertation]. Virginia Tech; 2010. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/10919/29007.

Council of Science Editors:

Ordonez-Delgado B. An Embedded Toeplitz Problem. [Doctoral Dissertation]. Virginia Tech; 2010. Available from: http://hdl.handle.net/10919/29007

8. Baldare, Alexandre. Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques : Index theory for families of G-transversally elliptic operators.

Degree: Docteur es, Mathématiques et modélisation, 2018, Montpellier

URL: http://www.theses.fr/2018MONTS005

► Le problème de l'indice est de calculer l'indice d'un opérateur elliptique en termes topologiques. Ce problème fut résolu par M. Atiyah et I. Singer en… (more)

▼ Le problème de l'indice est de calculer l'indice d'un opérateur elliptique en termes topologiques. Ce problème fut résolu par M. Atiyah et I. Singer en 1963 dans "The index of elliptic operators on compact manifolds". Quelques années plus tard, ces auteurs ont fourni une nouvelle preuve dans "The index of elliptic operators I" permettant plusieurs généralisations et applications. La première est la prise en compte de l'action d'un groupe compact G, dans ce cadre on obtient une égalité dans l'anneau des représentations de G. Par la suite ils ont généralisé ce résultat au cadre des familles d'opérateurs elliptiques paramétrées par un espace compact dans "The index of elliptic operators IV", ici l'égalité vit dans la K-théorie de l'espace paramétrant la famille.Une autre généralisation importante est celle des opérateurs transversalement elliptiques par rapport à l'action d'un groupe G, c'est-à-dire elliptiques dans le sens transverse aux orbites de l'action d'un groupe sur une variété. Cette classe d'opérateurs a été étudié pour la première fois dans le cadre d'un opérateur P agissant sur une variété M par M. Atiyah (et I. Singer) dans "Elliptic operators and compact groups", en 1974. Dans cet article l'auteur définit une classe indice et montre qu'elle ne dépend que de la classe du symbole en K-théorie. Il montre ensuite qu'elle vérifie différents axiomes : action libre, multiplicativité et excision. Ces différents axiomes permettent alors de ramener le calcul de l'indice à un espace euclidien muni de l'action d'un tore. Par la suite, cette classe d'opérateurs a été étudier du point de vue de la K-théorie bivariante par P. Julg [1982] et plus récemment dans le cadre des actions propres sur une variété non compacte par G. Kasparov [2016].Dans cette thèse, nous nous intéressons aux familles d'opérateurs G-transversalement elliptiques. Nous définissons une classe indice en K-théorie bivariante de Kasparov. Nous vérifions qu'elle ne dépend que de la classe du symbole de la famille en K-théorie. Nous montrons que notre classe indice vérifie les propriétés d'action libre, de multiplicativité et d'excision espérées en K-théorie bivariante. Nous montrons ensuite un théorème d'induction et de compatibilité avec les applications de Gysin. Ces derniers théorèmes permettent de ramener le calcul de l'indice au cas d'une famille triviale pour l'action d'un tore comme dans le cadre d'un seul opérateur sur une variété. Nous démontrons ensuite qu'on peut associer à cette classe indice un caractère de Chern à coefficients distributionnels sur G à valeurs dans la cohomologie de de Rham de l'espace paramétrant lorsque c'est une variété. Pour ce faire, nous utilisons l'homologie locale de M. Puschnigg [2003] et une technique de M. Hilsum et G. Skandalis [1987]. Par la suite, nous nous intéressons aux formules de Berline et Vergne dans ce cadre. Avant de passer aux formules générales pour une famille d'opérateurs G-transversalment elliptiques, on commence par regarder si on obtient les mêmes formules dans le cadre elliptique. On montre… Advisors/Committee Members: Benameur, Moulay-Tahar (thesis director).

Subjects/Keywords: Théorie de l'indice; Familles d'opérateurs transversalement elliptiques; KK-Théorie; Représentation de groupe; Cohomologie équivariante; Index theory; Family of transversally elliptic operators; KK-Theory; Group representation; Equivariant cohomology

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APA (6^th Edition):

Baldare, A. (2018). Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques : Index theory for families of G-transversally elliptic operators. (Doctoral Dissertation). Montpellier. Retrieved from http://www.theses.fr/2018MONTS005

Chicago Manual of Style (16^th Edition):

Baldare, Alexandre. “Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques : Index theory for families of G-transversally elliptic operators.” 2018. Doctoral Dissertation, Montpellier. Accessed January 28, 2021. http://www.theses.fr/2018MONTS005.

MLA Handbook (7^th Edition):

Baldare, Alexandre. “Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques : Index theory for families of G-transversally elliptic operators.” 2018. Web. 28 Jan 2021.

Vancouver:

Baldare A. Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques : Index theory for families of G-transversally elliptic operators. [Internet] [Doctoral dissertation]. Montpellier; 2018. [cited 2021 Jan 28]. Available from: http://www.theses.fr/2018MONTS005.

Council of Science Editors:

Baldare A. Théorie de l'indice pour les familles d'opérateurs G-transversalement elliptiques : Index theory for families of G-transversally elliptic operators. [Doctoral Dissertation]. Montpellier; 2018. Available from: http://www.theses.fr/2018MONTS005

Penn State University

9. Dumitrascu, Constantin Dorin. A New Approach to Bivariant K-theory.

Degree: 2008, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/5876

► We construct a new bivariant theory, that we call KE-theory, which is intermediate between the KK-theory of Gennadi Kasparov, and the E-theory of Alain Connes… (more)

Subjects/Keywords: associative product; C*-algebras; KK-theory; E-theory

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APA (6^th Edition):

Dumitrascu, C. D. (2008). A New Approach to Bivariant K-theory. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/5876

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):

Dumitrascu, Constantin Dorin. “A New Approach to Bivariant K-theory.” 2008. Thesis, Penn State University. Accessed January 28, 2021. https://submit-etda.libraries.psu.edu/catalog/5876.

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

MLA Handbook (7^th Edition):

Dumitrascu, Constantin Dorin. “A New Approach to Bivariant K-theory.” 2008. Web. 28 Jan 2021.

Vancouver:

Dumitrascu CD. A New Approach to Bivariant K-theory. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Jan 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/5876.

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

Council of Science Editors:

Dumitrascu CD. A New Approach to Bivariant K-theory. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/5876

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

University of Victoria

10. Duwenig, Anna. Poincaré self-duality of A_θ.

Degree: Department of Mathematics and Statistics, 2020, University of Victoria

URL: http://hdl.handle.net/1828/11678

► The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was… (more)

Subjects/Keywords: irrational rotation algebra; KK-theory; abstract transversal; groupoid; Kronecker Flow; noncommutative torus; Poincaré duality; Kasparov product; unbounded operator; noncommutative geometry; bivariant K-theory

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APA (6^th Edition):

Duwenig, A. (2020). Poincaré self-duality of A_θ. (Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/11678

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):

Duwenig, Anna. “Poincaré self-duality of A_θ.” 2020. Thesis, University of Victoria. Accessed January 28, 2021. http://hdl.handle.net/1828/11678.

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

MLA Handbook (7^th Edition):

Duwenig, Anna. “Poincaré self-duality of A_θ.” 2020. Web. 28 Jan 2021.

Vancouver:

Duwenig A. Poincaré self-duality of A_θ. [Internet] [Thesis]. University of Victoria; 2020. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/1828/11678.

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

Council of Science Editors:

Duwenig A. Poincaré self-duality of A_θ. [Thesis]. University of Victoria; 2020. Available from: http://hdl.handle.net/1828/11678

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

11. Takata, Doman. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .

Degree: 2018, Kyoto University

URL: http://hdl.handle.net/2433/232217

Subjects/Keywords: infinite-dimensional manifolds; loop groups; Dirac operators; assembly maps; KK-theory; index theory

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APA (6^th Edition):

Takata, D. (2018). A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/232217

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):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Thesis, Kyoto University. Accessed January 28, 2021. http://hdl.handle.net/2433/232217.

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

MLA Handbook (7^th Edition):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Web. 28 Jan 2021.

Vancouver:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Internet] [Thesis]. Kyoto University; 2018. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/2433/232217.

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

Council of Science Editors:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Thesis]. Kyoto University; 2018. Available from: http://hdl.handle.net/2433/232217

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

Uppsala University

12. Söderberg, Alexander. Browsing the Web of Amplitudes.

Degree: Theoretical Physics, 2016, Uppsala University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-309989

► We begin by studying field-theory amplitude relations such as the Kleiss-Kuijf, Bern-Carrasco-Johansson, Kawai-Lewellen-Tye and the double copy construction, which are important ingredients in this… (more)

Subjects/Keywords: amplitude; amplitudes; relation; relations; browsing; web; bcj; kk; double; copy; zeroth; klt; single; valued; projection; quantum; field; theory; qft; string; type; I; II; heterotic; Other Physics Topics; Annan fysik

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APA (6^th Edition):

Söderberg, A. (2016). Browsing the Web of Amplitudes. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-309989

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):

Söderberg, Alexander. “Browsing the Web of Amplitudes.” 2016. Thesis, Uppsala University. Accessed January 28, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-309989.

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

MLA Handbook (7^th Edition):

Söderberg, Alexander. “Browsing the Web of Amplitudes.” 2016. Web. 28 Jan 2021.

Vancouver:

Söderberg A. Browsing the Web of Amplitudes. [Internet] [Thesis]. Uppsala University; 2016. [cited 2021 Jan 28]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-309989.

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

Council of Science Editors:

Söderberg A. Browsing the Web of Amplitudes. [Thesis]. Uppsala University; 2016. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-309989

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

13. Hudson, Daniel. K-theory correspondences and the Fourier-Mukai transform.

Degree: Department of Mathematics and Statistics, 2019, University of Victoria

URL: http://hdl.handle.net/1828/10837

► The goal of this thesis is to give an introduction to the geometric picture of bivariant K-theory developed by Emerson and Meyer building on the… (more)

Subjects/Keywords: K-Theory; Algebraic Topology; KK-Theory; Operator Algebras; Non-Commutative Geometry

…theory. In his paper “Equivariant KK-theory and the Novikov Conjecture” ([16]… …composes functions. Thus, one can think of KK-theory as being a generalization of group… …groups arises from a class in KK-theory. Kasparov’s theory is defined at the level of C… …is called a homology or cohomology theory, depending on whether the Fi are covariant or… …but the one we will focus on in this thesis is K-theory. Given a topological space X, the K…

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

APA (6^th Edition):

Hudson, D. (2019). K-theory correspondences and the Fourier-Mukai transform. (Masters Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/10837

Chicago Manual of Style (16^th Edition):

Hudson, Daniel. “K-theory correspondences and the Fourier-Mukai transform.” 2019. Masters Thesis, University of Victoria. Accessed January 28, 2021. http://hdl.handle.net/1828/10837.

MLA Handbook (7^th Edition):

Hudson, Daniel. “K-theory correspondences and the Fourier-Mukai transform.” 2019. Web. 28 Jan 2021.

Vancouver:

Hudson D. K-theory correspondences and the Fourier-Mukai transform. [Internet] [Masters thesis]. University of Victoria; 2019. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/1828/10837.

Council of Science Editors:

Hudson D. K-theory correspondences and the Fourier-Mukai transform. [Masters Thesis]. University of Victoria; 2019. Available from: http://hdl.handle.net/1828/10837

14. Mohsen, Omar. Deformation groupoids and applications : Groupoïdes de déformations et applications.

Degree: Docteur es, Mathématiques. Géométrie non commutative, 2018, Sorbonne Paris Cité

URL: http://www.theses.fr/2018USPCC200

►

Cette thèse est consacrée à l’étude de trois questions différentes concernant les groupoïdes de Lie et leurs applications. Le premier chapitre présente quelques préliminaires sur… (more)

▼

Cette thèse est consacrée à l’étude de trois questions différentes concernant les groupoïdes de Lie et leurs applications. Le premier chapitre présente quelques préliminaires sur les groupoïdes de Lie. Dans le chapitre 2, on exprime la déformation de Witten à l’aide d’une déformation au cone normal et la théorie de C∗-modules ce qui nous permet de retrouver les inégalités de Morse. Notre méthode se généralise au cas des feuilletages. Dans le chapitre 3, on donne une construction simple du groupoïde de déformation construit par Choi-Pönge et Van Erp-Yuncken. Rappelons que celui-ci décrit le calcule pseudo-différentiel inhomogène grâce au travail de Debord-Skandalis et Van Erp- Yuncken. Notre construction montre que le groupoïde de déformation est en fait une déformation au cone normal classique itérée. Dans le chapitre 4, suivant le travail de Antonini, Azzali et Skandalis, on construit un élément en KK-théorie équivariante qui permet d’exprimer directement les invariants de Chern-Simons en K-théorie. Dans l’appendice on donne quelques rappels sur la KK-théorie équivariante et la KK-théorie réelle introduite par Antonini, Azzali et Skandalis.

This thesis is devoted to the study of three different questions concerning Lie groupoids and their applications. The first chapter presents some preliminaries on Lie groupoids. In Chapter 2, Witten’s deformation is expressed using deformation to the normal cone construction and the theory of C∗-modules, which allows us to reprove the Morse inequalities. Our method is generalised to the case of foliations. In Chapter 3, we give a simple construction of the deformation groupoid built by Choi-Pönge and Van Erp-Yuncken. Recall that this groupoid describes the inhomogeneous pseudo-differential calculus thanks to the work of Debord-Skandalis and Van Erp-Yuncken. Our construction shows that the deformation groupoid is actually an iterated classical deformation to the normal cone. In Chapter 4, following the work of Antonini, Azzali and Skandalis, we construct an element in equivariant KK-theory that allows us to express the Chern-Simons invariants directly in K-theory. In the appendix we give some reminders about the equivariant KK-theory and the real KK-theory introduced by Antonini, Azzali and Skandalis.

Advisors/Committee Members: Skandalis, Georges (thesis director).

Subjects/Keywords: Déformation au cone normal; Déformation de Witten; Fonctions de Morse; Calcul pseudo-différentiel inhomogène; Invariants de Chern-Simons; Lie groupoids; Deformation to normal cone; Witten deformation; Morse functions; Inhomogeneous pseudo-differential calculus; KK-theory; Chern-Simons invariants

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

APA (6^th Edition):

Mohsen, O. (2018). Deformation groupoids and applications : Groupoïdes de déformations et applications. (Doctoral Dissertation). Sorbonne Paris Cité. Retrieved from http://www.theses.fr/2018USPCC200

Chicago Manual of Style (16^th Edition):

Mohsen, Omar. “Deformation groupoids and applications : Groupoïdes de déformations et applications.” 2018. Doctoral Dissertation, Sorbonne Paris Cité. Accessed January 28, 2021. http://www.theses.fr/2018USPCC200.

MLA Handbook (7^th Edition):

Mohsen, Omar. “Deformation groupoids and applications : Groupoïdes de déformations et applications.” 2018. Web. 28 Jan 2021.

Vancouver:

Mohsen O. Deformation groupoids and applications : Groupoïdes de déformations et applications. [Internet] [Doctoral dissertation]. Sorbonne Paris Cité; 2018. [cited 2021 Jan 28]. Available from: http://www.theses.fr/2018USPCC200.

Council of Science Editors:

Mohsen O. Deformation groupoids and applications : Groupoïdes de déformations et applications. [Doctoral Dissertation]. Sorbonne Paris Cité; 2018. Available from: http://www.theses.fr/2018USPCC200

Freie Universität Berlin

15. Mund, Jens Karl Heinz. Quantenfeldtheorie von Teilchen mit Zopfgruppenstatistik in 2+1 Dimensionen.

Degree: 1999, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-7561

► Die vorliegende Arbeit befaßt sich im Rahmen der lokalen Quantenphysik mit relativistischen Teilchen und Feldern in drei Raumzeit-Dimensionen, deren Statistik durch eine Darstellung der Zopfgruppe… (more)

▼ Die vorliegende Arbeit befaßt sich im Rahmen der lokalen Quantenphysik mit relativistischen Teilchen und Feldern in drei Raumzeit-Dimensionen, deren Statistik durch eine Darstellung der Zopfgruppe zu beschreiben ist - sogenannten Plektonen bzw., falls die Darstellung Abelsch ist, Anyonen. Insbesondere wurde die Frage nach der Existenz von freien anyonischen Feldern untersucht. In unserem Zusammenhang sollen hierunter Operatoren verstanden werden, die mit den `lokalen´ Feldalgebren affiliiert sind und nur Einteilchenvektoren aus dem Vakuum erzeugen. (Lokalisierbarkeit bezieht sich hier auf Gebiete, die sich entlang eines raumartigen Weges ins Unendliche erstrecken.) Unter einer schwachen Regularitätsbedingung an die Felder konnten dann Vertauschungsrelationen hergeleitet werden, die sich nicht mit der Zopfgruppenstatistik vertragen. Desweiteren wurden modellunabhängige Aussagen bezüglich des PCT-Operators und des Zusammenhangs von Spin und Statistik erhalten. Unter der Annahme, daß die Observablenalgebra das Bisognano-Wichmann-Theorem erfüllt, wurde ein `PCT´-Theorem für Plektonen hergeleitet. (Die PCT-Transformation beinhaltet in drei Dimensionen eine räumliche Spiegelung (P) nur an der x2-Achse.) Für Anyonen wird gezeigt, daß sich die Bisognano-Wichmann-Eigenschaft sogar, in `getwisteter´ Form, auf die Feldalgebra übertägt. Insbesondere stimmt der PCT- Operator bis auf einen Twistoperator mit der modularen Konjugation der Feldalgebra zu einem Standard-Keilgebiet überein. Hieraus konnte das Spin- Statistik-Theorem für Anyonen hergeleitet werden. Ferner wurde zur Klärung der Struktur des Hilbertraums der Streuzustände von Plektonen und Anyonen beigetragen. Diese ist bekannterweise fixiert durch die relevanten Darstellungen der Zopfgruppe und durch die Fusionsregeln, nach denen die von den Streuzuständen getragenen Ladungen bestimmt sind. Es wurden Mølleroperatoren W+ und W- vom Raum der aus- und der einlaufenden Streuzustände in einen Referenz-Hilbertraum angegeben, welche die physikalische Strahldarstellung der Poincarégruppe auf den Streuzustandsräumen in eine kanonische Strahldarstellung im Referenz-Hilbertraum übersetzen. Ein neues Ergebnis betrifft den `einlaufenden freien PCT-Operator´, d.h. das Produkt des PCT-Operators mit der S-Matrix S = ( W+)* W- : Auch der hierzu via W- äquivalente Konjugationsoperator im Referenz-Hilbertraum konnte angegeben werden. Im Falle von Anyonen sind die Fusionsregeln trivial und die relevanten Darstellungen der Zopfgruppe sind einfach durch einen Satz von komplexen (`Statistik´-) Phasen charakterisiert. Daher lieferten uns in diesem Fall die obigen Ergebnisse explizite Formeln für die Strahldarstellung der Poincarégruppe und den einlaufenden freien PCT-Operator. In Anbetracht der Bisognano-Wichmann-Eigenschaft haben wir hiermit insbesondere zu jedem Keilgebiet das Produkt des Tomita-Operators mit der S-Matrix bestimmt, also den `einlaufenden freien´ Tomita-Operator der anyonischen Feldalgebra. Advisors/Committee Members: n (gender), Professor Dr. Robert Schrader (firstReferee), Professor Dr. Bert Schroer (furtherReferee).

Subjects/Keywords: anyons; plektons; braid group statistics; scattering theory; free field; modular localization; 11.10.Cd; 11.10.Kk; 500 Naturwissenschaften und Mathematik::530 Physik::530 Physik

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

APA (6^th Edition):

Mund, J. K. H. (1999). Quantenfeldtheorie von Teilchen mit Zopfgruppenstatistik in 2+1 Dimensionen. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-7561

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):

Mund, Jens Karl Heinz. “Quantenfeldtheorie von Teilchen mit Zopfgruppenstatistik in 2+1 Dimensionen.” 1999. Thesis, Freie Universität Berlin. Accessed January 28, 2021. http://dx.doi.org/10.17169/refubium-7561.

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

MLA Handbook (7^th Edition):

Mund, Jens Karl Heinz. “Quantenfeldtheorie von Teilchen mit Zopfgruppenstatistik in 2+1 Dimensionen.” 1999. Web. 28 Jan 2021.

Vancouver:

Mund JKH. Quantenfeldtheorie von Teilchen mit Zopfgruppenstatistik in 2+1 Dimensionen. [Internet] [Thesis]. Freie Universität Berlin; 1999. [cited 2021 Jan 28]. Available from: http://dx.doi.org/10.17169/refubium-7561.

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

Council of Science Editors:

Mund JKH. Quantenfeldtheorie von Teilchen mit Zopfgruppenstatistik in 2+1 Dimensionen. [Thesis]. Freie Universität Berlin; 1999. Available from: http://dx.doi.org/10.17169/refubium-7561

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

Open Access Theses and Dissertations