Exotic Twisted Equivariant K-Theory

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 $Z$.

19 pages, revised, to appear in J. Geom. Phys