Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts

Abstract

We will study several subgroups of continuous full groups of one-sided topological Markov shifts from the view points of cohomology groups of full group actions on the shift spaces. We also study continuous orbit equivalence and strongly continuous orbit equivalence in terms of these subgroups of the continuous full groups and the cohomology groups.

arXiv comment24 pages

References in corpus (3)

• Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
• Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

Cited by in corpus (2)

• On a family of $C^{\ast }$-subalgebras of Cuntz-Krieger algebras
• One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz--Krieger algebras