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.
Inhyeop Yi
Ewha Womans University
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)
2012; 49(1): 109-126
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