Loop groups and twisted K-theory I

Daniel S. Freed; Michael J. Hopkins; Constantin Teleman

doi:10.1112/jtopol/jtr019

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arXiv · 0711.1906

Loop groups and twisted K-theory I

Daniel S. Freed·Michael J. Hopkins·Constantin Teleman

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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.

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BibTeX RIS

Daniel S. Freed, Michael J. Hopkins, Constantin Teleman. 2007-11-13. Loop groups and twisted K-theory I. https://doi.org/10.1112/jtopol%2Fjtr019

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