{
  "id": "2307.13970",
  "version": "v1",
  "published": "2023-07-26T06:10:25.000Z",
  "updated": "2023-07-26T06:10:25.000Z",
  "title": "Groups generated by Dehn Twists along fillings of surfaces",
  "authors": [
    "Rakesh Kumar"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $S_g$ denote a closed oriented surface of genus $g \\geq 2$. A set $\\Omega = \\{ c_1, \\dots, c_d\\}$ of pairwise non-homotopic simple closed curves on $S_g$ is called a filling system or simply a filling of $S_g$, if $S_g\\setminus \\Omega$ is a union of $\\ell$ topological discs for some $\\ell\\geq 1$. For $1\\leq i\\leq d$, let $T_{c_i}$ denotes the Dehn twist along $c_i$. In this article, we show that for each $d\\geq 2$, there exists a filling $\\Omega=\\{c_1,c_2,\\dots, c_d\\}$ of $S_g$ such that the group $\\langle T_{c_1}, T_{c_2},\\dots,T_{c_d}\\rangle$ is isomorphic to the free group of rank $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-26T06:10:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K20",
      "57M15",
      "05C10"
    ],
    "keywords": [
      "dehn twist",
      "pairwise non-homotopic simple closed curves",
      "free group",
      "filling system",
      "oriented surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}