Metrizable universal minimal flows of Polish groups have a comeagre orbit

By Itaï Ben Yaacov, Julien Melleray, Todor Tsankov. Geometric and Functional Analysis, 2016

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We prove that, whenever G is a Polish group with metrizable universal minimal flow M(G), there exists a comeagre orbit in M(G). It then follows that there exists an extremely amenable, closed, co-precompact subgroup G* of G such that M(G)=G/G∗^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M(G) = \widehat{G/G^*}}$$\end{document}.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/539e519d4ef34ec2e3bf34a7140784698bac458f