{
  "id": "1711.05665",
  "version": "v1",
  "published": "2017-11-15T16:58:36.000Z",
  "updated": "2017-11-15T16:58:36.000Z",
  "title": "A characterization of Fuchsian actions by topological rigidity",
  "authors": [
    "Kathryn Mann",
    "Maxime Wolff"
  ],
  "comment": "Companion paper to arXiv:1710.04902 [math.GT] by the same authors. This article gives a simple proof of a special case",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that any rigid representation of $\\pi_1\\Sigma_g$ in $\\mathrm{Homeo}_+(S^1)$ with Euler number at least $g$ is necessarily semi-conjugate to a discrete, faithful representation into $\\mathrm{PSL}(2,\\mathbb{R})$. Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions by a topological rigidity property. Though independent, this work can be read as an introduction to the companion paper {\\em rigidity and geometricity for surface group actions on the circle}, by the same authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-15T16:58:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "surface group actions",
      "precisely characterizes fuchsian actions",
      "euler number",
      "companion paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}