Loop Groups and Twisted K-Theory II

Details Loop Groups and Twisted K-Theory II Loop Groups and Twisted K-Theory II

2005-11-09

arxiv.org/abs/math/0511232v2

Mathematics

Algebraic Topology

60 pages; minor corrections in version 2

Scientific paper

This is the second 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. We introduce the Dirac family of Fredholm operators associated to a positive energy representation of a loop group. It determines a map from isomorphism classes of representations to twisted K-theory, which we prove is an isomorphism if $G$ is connected with torsion-free fundamental group. We also introduce a Dirac family for finite dimensional representations of compact Lie groups; it is closely related to both the Kirillov correspondence and the equivariant Thom isomorphism. In Part III (math.AT/0312155) we extend the proof of our main theorem to arbitrary compact Lie groups G and provide supplements in various directions. In Part I (arXiv:0711.1906) we develop twisted equivariant K-theory and carry out some of the computations needed here. We refer to the announcements math.AT/0312155 and math.AT/0206237 for further expository material and motivation.

Affiliated with

Also associated with

No associations

Rating

Loop Groups and Twisted K-Theory II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Loop Groups and Twisted K-Theory II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Loop Groups and Twisted K-Theory II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-104304