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arXiv · 1211.5006

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

Bernhard Burgstaller
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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.

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Bernhard Burgstaller. 2012-11-21. Equivariant $KK$-theory of $r$-discrete groupoids and inverse semigroups. https://arxiv.org/abs/1211.5006

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