Loop groups and twisted K-theory I
Algebraic Topology
2014-02-26 v1 High Energy Physics - Theory
K-Theory and Homology
Representation Theory
Abstract
This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. In this paper we set up the foundations of twisted equivariant K-groups, and more generally twisted K-theory of groupoids. We establish enough basic properties to make effective computations. Using the Mayer-Vietoris spectral sequence we compute the twisted equivariant K-groups of a compact connected Lie group G with torsion free fundamental group. We relate this computation to the representation theory of the loop group at a level related to the twisting.
Cite
@article{arxiv.0711.1906,
title = {Loop groups and twisted K-theory I},
author = {Daniel S. Freed and Michael J. Hopkins and Constantin Teleman},
journal= {arXiv preprint arXiv:0711.1906},
year = {2014}
}