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.
| Original language | English |
|---|---|
| Pages (from-to) | 133-146 |
| Number of pages | 14 |
| Journal | Bulletin of the Korean Mathematical Society |
| Volume | 58 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2021 |
Bibliographical note
Funding Information:Received January 18, 2020; Revised September 27, 2020; Accepted October 16, 2020. 2010 Mathematics Subject Classification. 37B05, 37A20, 37C85, 20M30, 46L35. Key words and phrases. Self-similar group, continuous orbit equivalence, inverse semigroup, groupoid. 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).
Publisher Copyright:
© 2021 Korean Mathematical Society.