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arXiv · 2109.12831

Continuous orbit equivalence of semigroup actions

Xiangqi Qiang·Chengjun Hou
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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.

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Xiangqi Qiang, Chengjun Hou. 2021-09-27. Continuous orbit equivalence of semigroup actions. https://arxiv.org/abs/2109.12831

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