{
  "id": "1810.12489",
  "version": "v1",
  "published": "2018-10-30T02:09:09.000Z",
  "updated": "2018-10-30T02:09:09.000Z",
  "title": "Geodesics in the mapping class group",
  "authors": [
    "Kasra Rafi",
    "Yvon Verberne"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We construct explicit examples of geodesics in the mapping class group and show that the shadow of a geodesic in mapping class group to the curve graph does not have to be a quasi-geodesic. We also show that the quasi-axis of a pseudo-Anosov element of the mapping class group may not have the strong contractibility property. Specifically, we show that, after choosing a generating set carefully, one can find a pseudo-Anosov homeomorphism f, a sequence of points w_k and a sequence of radii r_k so that the ball B(w_k, r_k) is disjoint from a quasi-axis a of f, but for any projection map from mapping class group to a, the diameter of the image of B(w_k, r_k) grows like log(r_k).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-30T02:09:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E30",
      "20F34",
      "57M07"
    ],
    "keywords": [
      "mapping class group",
      "construct explicit examples",
      "strong contractibility property",
      "pseudo-anosov element",
      "curve graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}