Exotic Twisted Equivariant K-Theory

TL;DR

This paper develops a new form of twisted equivariant K-theory for loop spaces, incorporating gerbes with connection, and introduces a Chern character linking it to twisted cohomology, with localization properties.

Contribution

It introduces exotic twisted $ ext{T}$-equivariant K-theory for loop spaces based on gerbes, and defines a Chern character mapping to twisted cohomology with localization features.

Findings

Defines exotic twisted $ ext{T}$-equivariant K-theory for loop spaces.

Constructs an exotic twisted $ ext{T}$-equivariant Chern character.

Shows localization to twisted cohomology of $Z$.

Abstract

In this paper we introduce exotic twisted $\mathbb T$-equivariant K-theory of loop space $LZ$ depending on the (typically non-flat) holonomy line bundle ${\mathcal L}^B$ on $LZ$ induced from a gerbe with connection $B$ on $Z$. We also define exotic twisted $\mathbb T$-equivariant Chern character that maps the exotic twisted $\mathbb T$-equivariant K-theory of $LZ$ into the exotic twisted $\mathbb T$-equivariant cohomology as defined in an earlier paper of ours, and which localises to twisted cohomology of $Z$.