Conjugacy of local homeomorphisms via groupoids and C*-algebras
arXiv:2105.00479 · doi:10.1017/etds.2022.50
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.
arXiv comment19 pages. This version matches the version in Ergodic Theory and Dynamical Systems
References in corpus (17)
- Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
- The Path Space of a Directed Graph
- Cuntz-like algebras
- Graph algebras and orbit equivalence
- Diagonal-preserving gauge-invariant isomorphisms of graph -algebras
- Cuntz-Pimsner C*-algebras associated with subshifts
- Reconstruction of groupoids and C*-rigidity of dynamical systems
- Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids
- Groupoid models for the C*-algebras of topological higher-rank graphs
- Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids
- One-sided shift spaces over infinite alphabets
- C*-algebras, groupoids and covers of shift spaces
- Refined moves for structure-preserving isomorphism of graph C*-algebras
- Simplicity of twisted C*-algebras of Deaconu--Renault groupoids
- On a family of -subalgebras of Cuntz-Krieger algebras
- One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz--Krieger algebras
- One-sided topological conjugacy of normal subshifts and gauge actions on the associated -algebras