Loop groups and twisted Ktheory I
Abstract
This is the first in a series of papers investigating the relationship between the twisted equivariant Ktheory 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 Kgroups, and more generally twisted Ktheory of groupoids. We establish enough basic properties to make effective computations. Using the MayerVietoris spectral sequence we compute the twisted equivariant Kgroups 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1906
 Bibcode:
 2007arXiv0711.1906F
 Keywords:

 Mathematics  Algebraic Topology;
 High Energy Physics  Theory;
 Mathematics  KTheory and Homology;
 Mathematics  Representation Theory;
 19L47;
 22E67 (Primary);
 19K99 (Secondary)
 EPrint:
 doi:10.1112/jtopol/jtr019