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Given a topological group

$G$ , one may be interested in understanding its possible minimal actions. This can be partially achieved by calculating the universal minimal flow (UMF) of

$G$ . The UMF is the (unique)

$G$ -minimal system which factors onto all

$G$ -minimal systems. Answering a question of Uspenskij (2000), we prove that if

$X$ is a closed manifold of dimension

$2$ or higher or the Hilbert cube, then the universal minimal flow of

$Homeo(X)$ , the group of homeomorphisms of

$X$ equipped with the compact-open topology, is not metrizable.
This is joint work with Todor Tsankov and Andy Zucker.