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Continuous orbit equivalences on self-similar groups

이인협
대한수학회 (The Korean Mathematical Society)|2021.01|대한수학회보 (Bulletin of the KMS)|제58권 제1호|pp. 133-146|DOI 10.4134/BKMS.b200055

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키워드

inverse semigroupgroupoidSelf-similar groupcontinuous orbit equivalence
주제분류수학

초록

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.

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.

참고문헌 (20)

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