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The notion of continuous orbit equivalence in one-sided topological Markov shifts is introduced, and its basic properties are presented. The continuous full group \(\Gamma _A\) of a one-sided topological Markov shift \((X_A,\sigma _A)\) is introduced and proved to be a countably infinite non-amenable discrete group. It is regarded as a generalization of Higman–Thompson groups.

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Continuous Orbit Equivalence

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  • 发表日期：

    2025年

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  • Kengo Matsumoto

摘要

The notion of continuous orbit equivalence in one-sided topological Markov shifts is introduced, and its basic properties are presented. The continuous full group \(\Gamma _A\) of a one-sided topological Markov shift \((X_A,\sigma _A)\) is introduced and proved to be a countably infinite non-amenable discrete group. It is regarded as a generalization of Higman–Thompson groups.