Matui's AH conjecture for Graph Groupoids
Operator Algebras
2020-04-01 v1 Group Theory
K-Theory and Homology
Abstract
We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui's result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the -theory of its groupoid -algebra.
Cite
@article{arxiv.2003.14055,
title = {Matui's AH conjecture for Graph Groupoids},
author = {Petter Nyland and Eduard Ortega},
journal= {arXiv preprint arXiv:2003.14055},
year = {2020}
}
Comments
43 pages, 3 figures