2000 character limit reached
Ample groupoid homology and étale correspondences (2304.13473v3)
Published 26 Apr 2023 in math.KT and math.OA
Abstract: We show that \'etale 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 \'etale correspondences.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Collections
Sign up for free to add this paper to one or more collections.