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arXiv · 1902.06046

A generalized type semigroup and dynamical comparison

Xin Ma
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Abstract

In this paper, we construct a semigroup associated to an action of countable discrete group on a compact Hausdorff space, that can be regarded as a higher dimensional generalization of the type semigroup. Using this generalized type semigroup we obtain a new characterization of dynamical comparison. This answers a question of Kerr and Schafhauser. In addition, this paper suggests a definition of comparison for dynamical systems in which neither necessarily the acting group is amenable nor the action is minimal.

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Xin Ma. 2019-02-16. A generalized type semigroup and dynamical comparison. https://doi.org/10.1017/etds.2020.28

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