Abstract
We introduce notions of continuous orbit equivalence and strong (respective, weak) continuous orbit equivalence for automorphism systems of étale equivalence relations, and characterize them in terms of the semi-direct product groupoids, as well as their reduced groupoid $C^{*}$-algebras and the associated $C^{*}$-automorphism systems of group actions or coactions on them. In particular, we study topological rigidity of expansive automorphism actions on compact (connected) metrizable groups.
Funding Statement
This work was supported by the NSF of China (Grant No. 12271469, 11771379, 11971419).
Acknowledgments
The authors would like to thank the referees for reading this paper carefully and putting forward many valuable comments and suggestions.
Citation
Xiangqi Qiang. Chengjun Hou. "Continuous Orbit Equivalence for Automorphism Systems of Equivalence Relations." Taiwanese J. Math. 28 (1) 95 - 124, February, 2024. https://doi.org/10.11650/tjm/231105
Information
