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arXiv · 2008.08471

Topological dynamics beyond Polish groups

Gianluca Basso·Andy Zucker
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Abstract

When $G$ is a Polish group, metrizability of the universal minimal flow has been shown to be a robust dividing line in the complexity of the topological dynamics of $G$. We introduce a class of groups, the CAP groups, which provides a neat generalization of this dividing line to all topological groups. We prove a number of characterizations of this class, having very different flavors, and use these to prove that the class of CAP groups enjoys a number of nice closure properties. As a concrete application, we compute the universal minimal flow of the homeomorphism groups of several scattered topological spaces, building on recent work of Gheysens.

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Gianluca Basso, Andy Zucker. 2020-08-19. Topological dynamics beyond Polish groups. https://doi.org/10.4171/cmh/521

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