Minimal surjective local homeomorphisms of finite-dimensional compact spaces give Deaconu-Renault groupoids with dynamical comparison, yielding UCT Kirchberg algebras and, in the Cantor case, Matui's AH conjecture.
Amenable groupoids , volume 36 of Monographies de L'Enseignement Math\'ematique [Monographs of L'Enseignement Math\'ematique]
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Dynamical comparison for local homeomorphisms
Minimal surjective local homeomorphisms of finite-dimensional compact spaces give Deaconu-Renault groupoids with dynamical comparison, yielding UCT Kirchberg algebras and, in the Cantor case, Matui's AH conjecture.