Ample groupoid homology and étale correspondences

2023/04/26 by Miller, Alistair · 1 citation
#20J05 #46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2304.13473

Abstract

We show that étale correspondences between ample groupoids induce homomorphisms of homology groups. To complement this we explore the module categories of ample groupoids. We construct an induction-restriction adjunction for subgroupoids, which generates a procedure for building resolutions of arbitrary groupoid modules. These resolutions can be used to work with the Tor picture of groupoid homology, enabling explicit descriptions of the maps in homology induced by étale correspondences.

Cited by

• Chern character for torsion-free ample groupoids

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