{
  "id": "2008.08471",
  "version": "v1",
  "published": "2020-08-19T14:22:54.000Z",
  "updated": "2020-08-19T14:22:54.000Z",
  "title": "Topological dynamics beyond Polish groups",
  "authors": [
    "Gianluca Basso",
    "Andy Zucker"
  ],
  "categories": [
    "math.DS",
    "math.GR",
    "math.LO"
  ],
  "abstract": "When $G$ is a Polish group, metrizability of the universal minimal flow has been shown to be a robust dividing line in the complexity of the topological dynamics of $G$. We introduce a class of groups, the CAP groups, which provides a neat generalization of this dividing line to all topological groups. We prove a number of characterizations of this class, having very different flavors, and use these to prove that the class of CAP groups enjoys a number of nice closure properties. As a concrete application, we compute the universal minimal flow of the homeomorphism groups of several scattered topological spaces, building on recent work of Gheysens.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-19T14:22:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "22F50"
    ],
    "keywords": [
      "polish group",
      "topological dynamics",
      "universal minimal flow",
      "nice closure properties",
      "cap groups enjoys"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}