{
  "id": "1910.12220",
  "version": "v1",
  "published": "2019-10-27T09:41:04.000Z",
  "updated": "2019-10-27T09:41:04.000Z",
  "title": "Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable",
  "authors": [
    "Yonatan Gutman",
    "Todor Tsankov",
    "Andy Zucker"
  ],
  "categories": [
    "math.DS",
    "math.GN",
    "math.LO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-27T09:41:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal minimal flow",
      "homeomorphism groups",
      "high-dimensional manifolds",
      "metrizable",
      "meager orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}