Uniformly recurrent subgroups

Eli Glasner, Benjamin Weiss

Type: Other

Publication Date: 2015-01-01

Citations: 38

DOI: https://doi.org/10.1090/conm/631/12596

Abstract

We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in [2].Our main results are as follows.(i) It was shown in [28] that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model.In contrast we show here, using URS's, that for the lamplighter group there is an ergodic measure preserving action which does not admit a minimal model.(ii) For an arbitrary countable group G, every URS can be realized as the stability system of some topologically transitive G-system.

Locations

Contemporary mathematics - American Mathematical Society - View
arXiv (Cornell University) - View - PDF

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+	On the growth of Betti numbers of locally symmetric spaces	2011	Miklós Abért Nicolas Bergeron Ian Biringer Tsachik Gelander Nikolay Nikolov Jean Raimbault Iddo Samet
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