# Ample groupoids: equivalence, homology, and Matui's HK conjecture

@article{Farsi2018AmpleGE, title={Ample groupoids: equivalence, homology, and Matui's HK conjecture}, author={Carla Farsi and Alex Kumjian and David Pask and Aidan Sims}, journal={arXiv: Operator Algebras}, year={2018} }

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 pairwisecommuting 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 specialise to k-graph…

## 21 Citations

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