The ring structure for equivariant twisted K-theory

Details The ring structure for equivariant twisted K-theory The ring structure for equivariant twisted K-theory

2006-04-07

arxiv.org/abs/math/0604160v3

Mathematics

K-Theory and Homology

47 pages. To appear in Crelle

Scientific paper

We prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2-multiplicative. We also give an explicit construction of the transgression map $T_1: H^*(\Gamma;A) \to H^{*-1}((N\rtimes \Gamma;A)$ for any crossed module $N\to \Gamma$ and prove that any element in the image is $\infty$-multiplicative. As a consequence, we prove that, under some mild conditions, for a crossed module $N \to \gm$ and any $e \in \check{Z}^3(\Gamma;S^1)$, that the equivariant twisted K-theory group $K^*_{e,\Gamma}(N)$ admits a ring structure. As an application, we prove that for a compact, connected and simply connected Lie group G, the equivariant twisted K-theory group $K_{[c], G}^* (G)$ is endowed with a canonical ring structure $K^{i+d}_{[c],G}(G)\otimes K^{j+d}_{[c],G}(G)\to K^{i+j+d}_{[c], G}(G)$, where $d=dim G$ and $[c]\in H^2(G\rtimes G;S^1)$.

Affiliated with

Also associated with

No associations

Rating

The ring structure for equivariant 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 The ring structure for equivariant twisted K-theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The ring structure for equivariant twisted K-theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-723426