Conjugacy of local homeomorphisms via groupoids and C*-algebras

Kevin Aguyar Brix, Becky Armstrong, Toke Carlsen, Søren Eilers

Research output: Working paperPreprint


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.
Original languageEnglish
Number of pages19
Publication statusPublished - 2 May 2021


  • Conjugacy
  • Local homeomorphism
  • Deaconu–Renault system
  • Groupoid
  • C*- algebra


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