Twisted K-Theory and TQFT

TL;DR

This paper recalculates the equivariant twisted K-theory of compact Lie groups using stacks and explores how moduli spaces of flat connections relate to TQFT structures, building on prior foundational work.

Contribution

It provides a new stack-based framework for calculating twisted K-theory and links moduli spaces of flat connections to TQFT trivializations, extending previous results.

Findings

Recalculation of equivariant twisted K-theory using stacks

Establishment of TQFT structures on twisted K-groups

Connection between moduli spaces of flat connections and trivializations

Abstract

The goal of the present paper is the calculation of the equivariant twisted K-theory of a compact Lie group which acts on itself by conjugations, and elements of a TQFT-structure on the twisted K-groups. These results are originally due to D.S.Freed, M.J.Hopkins and C.Teleman. In this paper we redo their calculations in the framework of topological and differentiable stacks. We also show how moduli spaces of flat connections on surfaces give rise to trivializations of twists.