Bulletin of the
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Bull. Korean Math. Soc. 2021; 58(1): 133-146

Online first article January 5, 2021      Printed January 31, 2021

https://doi.org/10.4134/BKMS.b200055

Copyright © The Korean Mathematical Society.

Continuous orbit equivalences on self-similar groups

Inhyeop Yi

Ewha Womans University

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

MSC numbers: 37B05, 37A20, 37C85, 20M30, 46L35

Supported by: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048313)

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