{
  "id": "2108.06814",
  "version": "v1",
  "published": "2021-08-15T20:55:19.000Z",
  "updated": "2021-08-15T20:55:19.000Z",
  "title": "$C^1$ actions on the circle of finite index subgroups of $Mod(Σ_g)$, $Aut(F_n)$, and $Out(F_n)$",
  "authors": [
    "Kamlesh Parwani"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "Let $\\Sigma_{g}$ be a closed, connected, and oriented surface of genus $g \\geq 24$ and let $\\Gamma$ be a finite index subgroup of the mapping class group $Mod(\\Sigma_{g})$ that contains the Torelli group $\\mathcal{I}(\\Sigma_g)$. Then any orientation preserving $C^1$ action of $\\Gamma$ on the circle cannot be faithful. We also show that if $\\Gamma$ is a finite index subgroup of $Aut(F_n)$, when $n \\geq 8$, that contains the subgroup of IA-automorphisms, then any orientation preserving $C^1$ action of $\\Gamma$ on the circle cannot be faithful. Similarly, if $\\Gamma$ is a finite index subgroup of $Out(F_n)$, when $n \\geq 8$, that contains the Torelli group $\\mathcal{T}_n$, then any orientation preserving $C^1$ action of $\\Gamma$ on the circle cannot be faithful.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-15T20:55:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37C05",
      "20F65"
    ],
    "keywords": [
      "finite index subgroup",
      "torelli group",
      "orientation preserving",
      "mapping class group",
      "ia-automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}