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http://dx.doi.org/10.4134/BKMS.b200055

CONTINUOUS ORBIT EQUIVALENCES ON SELF-SIMILAR GROUPS  

Yi, Inhyeop (Department of Mathematics Education Ewha Womans University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.1, 2021 , pp. 133-146 More about this Journal
Abstract
For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.
Keywords
Self-similar group; continuous orbit equivalence; inverse semigroup; groupoid;
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