{
  "id": "2001.05522",
  "version": "v1",
  "published": "2020-01-15T19:30:44.000Z",
  "updated": "2020-01-15T19:30:44.000Z",
  "title": "Minimality of the action on the universal circle of uniform foliations",
  "authors": [
    "Sergio Fenley",
    "Rafael Potrie"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "Given a uniform foliation by Gromov hyperbolic leaves on a $3$-manifold, we show that the action of the fundamental group on the universal circle is minimal and transitive on pairs of different points. We also prove two other results: we prove that general uniform Reebless foliations are $\\mathbb{R}$-covered and we give a new description of the universal circle of $\\mathbb{R}$-covered foliations with Gromov hyperbolic leaves in terms of the JSJ decomposition of $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-15T19:30:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal circle",
      "uniform foliation",
      "gromov hyperbolic leaves",
      "minimality",
      "general uniform reebless foliations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}