Twisted $K$-theory

Details Twisted $K$-theory Twisted $K$-theory

2004-07-05

arxiv.org/abs/math/0407054v2

Mathematics

K-Theory and Homology

49 pages;some minor corrections have been made to the earlier version

Scientific paper

Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary $K$-theory. (We omit, however, its relations to classical cohomology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group $H^3_G(X;\Z)$. We also consider some basic examples of twisted $K$-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman.

Affiliated with

Also associated with

No associations

Rating

Twisted $K$-theory 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 Twisted $K$-theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Twisted $K$-theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-72873