TY - JOUR

T1 - Continuous orbit equivalences on self-similar groups

AU - Yi, Inhyeop

N1 - 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.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85100550025&partnerID=8YFLogxK

U2 - 10.4134/BKMS.b200055

DO - 10.4134/BKMS.b200055

M3 - Article

AN - SCOPUS:85100550025

VL - 58

SP - 133

EP - 146

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

SN - 1015-8634

IS - 1

ER -