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 -