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arXiv · 1307.1299

Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras

Kengo Matsumoto·Hiroki Matui
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Abstract

Let A,B be square irreducible matrices with entries in {0,1}. We will show that if the one-sided topological Markov shifts (X_A,σ_A) and (X_B,σ_B) are continuously orbit equivalent, then the two-sided topological Markov shifts (\bar X_A,\barσ_A) and (\bar X_B,\barσ_B) are flow equivalent, and hence det(id-A)=det(id-B). As a result, the one-sided topological Markov shifts (X_A,σ_A) and (X_B,σ_B) are continuously orbit equivalent if and only if the Cuntz-Krieger algebras O_A and O_B are isomorphic and det(id-A)=det(id-B).

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Kengo Matsumoto, Hiroki Matui. 2013-07-04. Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras. https://doi.org/10.1215/21562261-2801849

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