Twisted equivariant K-theory and equivariant T-duality

Dove, Thomas

dc.contributor.advisor	Schick, Thomas Prof. Dr.
dc.contributor.author	Dove, Thomas
dc.date.accessioned	2023-09-18T15:16:39Z
dc.date.available	2023-09-25T00:50:15Z
dc.date.issued	2023-09-18
dc.identifier.uri	http://resolver.sub.uni-goettingen.de/purl?ediss-11858/14882
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-10100
dc.format.extent	91	de
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject.ddc	510	de
dc.title	Twisted equivariant K-theory and equivariant T-duality	de
dc.type	doctoralThesis	de
dc.contributor.referee	Schick, Thomas Prof. Dr.
dc.date.examination	2023-08-30	de
dc.description.abstracteng	This thesis is about two things: twisted equivariant K-theory and equivariant topological T-duality. First, we prove a fixed point decomposition theorem for twisted equivariant K-theory, generalising a result of Atiyah and Segal. This is a description of joint work with Thomas Schick and Mario Velásquez. Next, we generalise the Atiyah-Segal completion theorem for families of subgroups to the twisted case. This is an extension of work by Lahtinen, who generalised the original Atiyah-Segal theorem to the twisted case. Thirdly, we explicitly define the pushforward map in twisted equivariant K-theory and apply it to the case of equivariant principal circle bundles.This is an application of techniques that are well-known to non-commutative geometers but have not gained widespread attention among topologists. In the second half of the thesis, we formulate equivariant topological T-duality and prove that the T-duality transformation in twisted equivariant K-theory is an isomorphism for all compact Lie groups.	de
dc.contributor.coReferee	Meyer, Ralf Prof. Dr.
dc.subject.eng	Algebraic Topology	de
dc.subject.eng	K-Theory	de
dc.subject.eng	T-Duality	de
dc.subject.eng	Principal Bundles	de
dc.identifier.urn	urn:nbn:de:gbv:7-ediss-14882-5
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.description.embargoed	2023-09-25	de
dc.identifier.ppn	1860027024
dc.notes.confirmationsent	Confirmation sent 2023-09-18T19:45:01	de

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