English

Katsura--Exel--Pardo Groupoids and the AH~Conjecture

Operator Algebras 2021-09-17 v1 Group Theory K-Theory and Homology

Abstract

It is proven that Matui's AH~conjecture is true for Katsura--Exel--Pardo groupoids GA,B\mathcal{G}_{A,B} associated to integral matrices AA and BB. This conjecture relates the topological full group of an ample groupoid with the homology groups of the groupoid. We also give a criterion under which the topological full group [[GA,B]][[\mathcal{G}_{A,B}]] is finitely generated.

Keywords

Cite

@article{arxiv.2007.06638,
  title  = {Katsura--Exel--Pardo Groupoids and the AH~Conjecture},
  author = {Petter Nyland and Eduard Ortega},
  journal= {arXiv preprint arXiv:2007.06638},
  year   = {2021}
}