{
  "id": "2208.02461",
  "version": "v1",
  "published": "2022-08-04T05:12:26.000Z",
  "updated": "2022-08-04T05:12:26.000Z",
  "title": "The homeomorphism group of the universal Knaster continuum",
  "authors": [
    "Sumun Iyer"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.LO",
    "math.CO",
    "math.DS"
  ],
  "abstract": "We define a projective Fraiss\\'e family whose limit approximates the universal Knaster continuum. The family is such that the group $\\textrm{Aut}(\\mathbb{K})$ of automorphisms of the Fraiss\\'e limit is a dense subgroup of the group, $\\textrm{Homeo}(K)$, of homeomorphisms of the universal Knaster continuum. We prove that both $\\textrm{Aut}(\\mathbb{K})$ and $\\textrm{Homeo}(K)$ have universal minimal flow homeomorphic to the universal minimal flow of the free abelian group on countably many generators. The computation involves proving that both groups contain an open, normal subgroup which is extremely amenable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-04T05:12:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "54F15",
      "37B05",
      "05D10",
      "03C98"
    ],
    "keywords": [
      "universal knaster continuum",
      "homeomorphism group",
      "universal minimal flow homeomorphic",
      "free abelian group",
      "fraisse limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}