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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… Click to show full abstract
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.
Keywords:
generalized type;
semigroup dynamical;
semigroup;
type semigroup;
dynamical comparison;
comparison
Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2021
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Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!