Full groups of one-sided topological Markov shifts

Abstract

Let $(X_A,{\sigma }_A)$ be the right one-sided topological Markov shift for an irreducible matrix with entries in $\{0,1\}$, and ${\Gamma }_A$ the continuous full group of $(X_A,{\sigma }_A)$. For two irreducible matrices $A$ and $B$ with entries in $\{0,1\}$, it will be proved that the continuous full groups ${\Gamma }_A$ and ${\Gamma }_B$ are isomorphic as abstract groups if and only if their one-sided topological Markov shifts $(X_A,{\sigma }_A)$ and $(X_B,{\sigma }_B)$ are continuously orbit equivalent.

24 pages

Cited by in corpus (2)

• Topological full groups of one-sided shifts of finite type
• Strongly continuous orbit equivalence of one-sided topological Markov shifts