Twisted equivariant K-theory and equivariant T-duality

by Thomas Dove
Doctoral thesis
Date of Examination:2023-08-30
Date of issue:2023-09-18
Advisor:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Ralf Meyer
Persistent Address: http://dx.doi.org/10.53846/goediss-10100

 

 

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Abstract

English

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.
Keywords: Algebraic Topology; K-Theory; T-Duality; Principal Bundles
 
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