Continuous orbit equivalence of semigroup actions
Operator Algebras
2021-09-28 v1 Dynamical Systems
Abstract
In this paper, we consider semigroup actions of discrete countable semigroups on compact spaces by surjective local homeomorphisms. We introduce notions of continuous one-sided orbit equivalence and continuous orbit equivalence for semigroup actions, and characterize them in terms of the corresponding semi-groupoids and transformation groupoids respectively. Finally, we consider the case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of group actions.
Cite
@article{arxiv.2109.12831,
title = {Continuous orbit equivalence of semigroup actions},
author = {Xiangqi Qiang and Chengjun Hou},
journal= {arXiv preprint arXiv:2109.12831},
year = {2021}
}