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

2012/11/21 by Bernhard Burgstaller, Burgstaller, Bernhard
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA

paper · pdf · doi:10.48550/arxiv.1211.5006

arxiv created 2012/11/21 · arxiv updated 2012/11/22

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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