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Ample groupoid homology and \'etale correspondences
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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.
Forward citations
Cited by 2 Pith papers
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Homology of Steinberg algebras
Hochschild and cyclic homology of Steinberg algebras of ample groupoids decompose in terms of groupoid homology, and for Exel-Pardo algebras these invariants and K-theory are computed by explicit cones and exact sequences.
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Cohomology of ample groupoids
The module-based cochain complex for ample groupoids computes the same cohomology groups as the standard continuous cocycle cohomology.
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