TY  - JOUR
AB  - We investigate the homology of ample Hausdorff groupoids. We establish that a number of notions of equivalence of groupoids appearing in the literature coincide for ample Hausdorff groupoids, and deduce that they all preserve groupoid homology. We compute the homology of a Deaconu–Renault groupoid associated to k pairwise-commuting local homeomorphisms of a zero-dimensional space, and show that Matui’s HK conjecture holds for such a groupoid when k is one or two. We specialize to k-graph groupoids, and show that their homology can be computed in terms of the adjacency matrices, using a chain complex developed by Evans. We show that Matui’s HK conjecture holds for the groupoids of single vertex k-graphs which satisfy a mild joint-coprimality condition. We also prove that there is a natural homomorphism from the categorical homology of a k-graph to the homology of its groupoid.
AU  - Farsi, Carla
AU  - Kumjian, Alex
AU  - Pask, David
AU  - Sims, Aidan
DA  - 2019
DO  - 10.17879/53149724091
LA  - eng
IS  - Münster Journal of Mathematics
M2  - 411
PY  - 2019
SP  - 411-451
T2  - Münster Journal of Mathematics
TI  - Ample groupoids: Equivalence, homology, and Matui's HK conjecture
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:6-53149724313
Y2  - 2024-12-26T18:05:35
ER  -