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arXiv · 1702.07101

Realizing uniformly recurrent subgroups

Nicolás Matte Bon·Todor Tsankov
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Abstract

We show that every uniformly recurrent subgroup of a locally compact group is the family of stabilizers of a minimal action on a compact space. More generally, every closed invariant subset of the Chabauty space is the family of stabilizers of an action on a compact space on which the stabilizer map is continuous everywhere. This answers a question of Glasner and Weiss. We also introduce the notion of a universal minimal flow relative to a uniformly recurrent subgroup and prove its existence and uniqueness.

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Nicolás Matte Bon, Todor Tsankov. 2017-02-23. Realizing uniformly recurrent subgroups. https://arxiv.org/abs/1702.07101

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