A generalized type semigroup and dynamical comparison

In this paper, we construct and study a semigroup associated to an action of a countable discrete group on a compact Hausdorff space that can be regarded as a higher dimensional generalization of the type semigroup. We study when this semigroup is almost unperforated. This leads to a new characteriz...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2021-07, Vol.41 (7), p.2148-2165, Article 2148
Main Author: MA, XIN
Format: Article
Language:English
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Original Article
Semigroups
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Summary:In this paper, we construct and study a semigroup associated to an action of a countable discrete group on a compact Hausdorff space that can be regarded as a higher dimensional generalization of the type semigroup. We study when this semigroup is almost unperforated. This leads to a new characterization of dynamical comparison and thus answers a question of Kerr and Schafhauser. In addition, this paper suggests a definition of comparison for dynamical systems in which neither the acting group is necessarily amenable nor the action is minimal.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2020.28