Equivariant $KK$-theory of $r$-discrete groupoids and inverse semigroups

Bernhard Burgstaller

Equivariant $KK$-theory of $r$-discrete groupoids and inverse semigroups

K-Theory and Homology 2012-11-22 v1 Operator Algebras

Authors: Bernhard Burgstaller

Abstract

For an $r$ -discrete Hausdorff groupoid ${\cal G}$ and an inverse semigroup $S$ of slices of ${\cal G}$ there is an isomorphism between ${\cal G}$ -equivariant $KK$ -theory and compatible $S$ -equivariant $KK$ -theory. We use it to define descent homomorphisms for $S$ , and indicate a Baum--Connes map for inverse semigroups. Also findings by Khoshkam and Skandalis for crossed products by inverse semigroups are reflected in $KK$ -theory.

Keywords

equivariant KK-theory r-discrete groupoids inverse semigroups isomorphism descent homomorphisms Baum-Connes map crossed products

Cite

@article{arxiv.1211.5006,
  title  = {Equivariant $KK$-theory of $r$-discrete groupoids and inverse semigroups},
  author = {Bernhard Burgstaller},
  journal= {arXiv preprint arXiv:1211.5006},
  year   = {2012}
}

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