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

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• On the Topology and Flux of T-Dual Manifolds
• Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality
• Twisted chiral de Rham complex, generalized geometry, and T-duality
• Equivariant, string and leading order characteristic classes associated to fibrations
• T-duality in an H-flux: exchange of momentum and winding