Ample groupoid homology and étale correspondences

  • Alistair Miller

    University of Southern Denmark, Odense M, Denmark
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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.

Cite this article

Alistair Miller, Ample groupoid homology and étale correspondences. J. Noncommut. Geom. 19 (2025), no. 2, pp. 657–677

DOI 10.4171/JNCG/569