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arXiv · 1910.12220

Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable

Yonatan Gutman·Todor Tsankov·Andy Zucker
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Abstract

Answering a question of Uspenskij, we prove that if $X$ is a closed manifold of dimension $2$ or higher or the Hilbert cube, then the universal minimal flow of $\mathrm{Homeo}(X)$ is not metrizable. In dimension $3$ or higher, we also show that the minimal $\mathrm{Homeo}(X)$-flow consisting of all maximal, connected chains in $X$ has meager orbits.

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Yonatan Gutman, Todor Tsankov, Andy Zucker. 2021-01-07. Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable. https://arxiv.org/abs/1910.12220

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