Ample groupoid homology and \'etale correspondences
K-Theory and Homology
2024-09-09 v3 Operator Algebras
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.
Keywords
Cite
@article{arxiv.2304.13473,
title = {Ample groupoid homology and \'etale correspondences},
author = {Alistair Miller},
journal= {arXiv preprint arXiv:2304.13473},
year = {2024}
}
Comments
Version in the Journal of Noncommutative Geometry, corrected an inaccuracy in the final remark, 17 pages