Equivariant $\KK$-theory for generalised actions and Thom isomorphism in groupoid twisted $\K$-theory
K-Theory and Homology
2013-10-16 v2 Algebraic Topology
Operator Algebras
Abstract
We develop equivariant KK-theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce Stiefel-Whitney classes for real or complex equivariant vector bundles over locally compact groupoids to establish the Thom isomorphism theorem in twisted groupoid K-theory.
Keywords
Cite
@article{arxiv.1305.2495,
title = {Equivariant $\KK$-theory for generalised actions and Thom isomorphism in groupoid twisted $\K$-theory},
author = {El-kaïoum M. Moutuou},
journal= {arXiv preprint arXiv:1305.2495},
year = {2013}
}
Comments
21 pages, abstract changed, introductory exposition improved, minor corrections. Accepted for publication in J. K-theory