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

2019/10/27 by Yonatan Gutman, Gutman, Yonatan, Todor Tsankov +3 · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1910.12220

Abstract

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

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