{
  "id": "1802.04507",
  "version": "v1",
  "published": "2018-02-13T08:38:31.000Z",
  "updated": "2018-02-13T08:38:31.000Z",
  "title": "Minimal asymptotic translation lengths of Torelli groups and pure braid groups on curve graph",
  "authors": [
    "Hyungryul Baik",
    "Hyunshik Shin"
  ],
  "comment": "12 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "In this paper, we show that the minimal asymptotic translation length of the Torelli group $\\mathcal{I}_g$ of the surface $S_g$ of genus $g$ on the curve graph asymptotically behaves like $1/g$, contrary to the mapping class group $Mod(S_g)$, which behaves like $1/g^2$. We also show that the minimal asymptotic translation length of the pure braid group $PB_n$ on the curve graph asymptotically behaves like $1/n$, contrary to the braid group $B_n$, which behaves like $1/n^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-13T08:38:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "37E30",
      "30F60",
      "32G15"
    ],
    "keywords": [
      "minimal asymptotic translation length",
      "pure braid group",
      "torelli group",
      "curve graph asymptotically behaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}