Ample groupoid homology and étale correspondences

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1. Verfasser: Miller, Alistair
Format: Preprint
Veröffentlicht: 2023
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author Miller, Alistair
author_facet Miller, Alistair
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2304_13473
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Ample groupoid homology and étale correspondences
Miller, Alistair
K-Theory and Homology
Operator Algebras
20J05, 46L80
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.
title Ample groupoid homology and étale correspondences
topic K-Theory and Homology
Operator Algebras
20J05, 46L80
url https://arxiv.org/abs/2304.13473