Continuous Orbit Equivalence for Automorphism Systems of Equivalence Relations
Continuous Orbit Equivalence for Automorphism Systems of Equivalence Relations
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. …