{
  "id": "2212.09891",
  "version": "v1",
  "published": "2022-12-19T22:26:49.000Z",
  "updated": "2022-12-19T22:26:49.000Z",
  "title": "On Translation Lengths of Pseudo-Anosov Maps on the Curve Graph",
  "authors": [
    "Hyungryul Baik",
    "Changsub Kim"
  ],
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichm\\\"uller space, (c) giving a partial answer of how much powers will be needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-19T22:26:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "37E30"
    ],
    "keywords": [
      "curve graph",
      "pseudo-anosov map",
      "stable translation length",
      "dehn twists",
      "filling curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}