Conjugacy of local homeomorphisms via groupoids and C*-algebras

Abstract

We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include self-covering maps, one-sided shifts of finite type and, more generally, the boundary-path spaces of directed and topological graphs. We characterise topological conjugacy of these systems in terms of isomorphisms of their associated groupoids and C*-algebras. This significantly generalises recent work of Matsumoto and of the second- and third-named authors.

19 pages. This version matches the version in Ergodic Theory and Dynamical Systems

References in corpus (5)

• Groupoid models for the C*-algebras of topological higher-rank graphs
• Simplicity of twisted C*-algebras of Deaconu--Renault groupoids
• One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz--Krieger algebras
• On a family of $C^{\ast }$-subalgebras of Cuntz-Krieger algebras
• One-sided topological conjugacy of normal subshifts and gauge actions on the associated $C^{\ast }$-algebras

Cited by in corpus (3)

• Splittings for C*-correspondences and strong shift equivalence
• A correspondence between surjective local homeomorphisms and a family of separated graphs
• On strong shift equivalence for row-finite graphs and C*-algebras