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

Kengo Matsumoto

doi:10.3934/dcds.2021139

Article Contents

2022, Volume 42, Issue 2: 841-862. Doi: 10.3934/dcds.2021139

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

Kengo Matsumoto

Department of Mathematics, Joetsu University of Education, Joetsu, 943-8512, Japan

Received: March 31, 2021

Revised: July 31, 2021

Early access: September 2021

Published: February 2022

The author is supported by JSPS KAKENHI Grant Numbers 15K04896, 19K03537

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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.

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Mathematics Subject Classification: Primary: 37A55, 37B10; Secondary: 46L35.

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