{
  "id": "1410.4886",
  "version": "v1",
  "published": "2014-10-17T23:24:24.000Z",
  "updated": "2014-10-17T23:24:24.000Z",
  "title": "The curves not carried",
  "authors": [
    "Vaibhav Gadre",
    "Saul Schleimer"
  ],
  "comment": "12 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Suppose $\\tau$ is a train track on a surface $S$. Let $C(\\tau)$ be the set of isotopy classes of simple closed curves carried by $\\tau$. Masur and Minsky [2004] prove $C(\\tau)$ is quasi-convex inside the curve complex $C(S)$. We prove the complementary set $C(S) - C(\\tau)$ is also quasi-convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-17T23:24:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "30F60",
      "20F65"
    ],
    "keywords": [
      "curve complex",
      "train track",
      "complementary set",
      "quasi-convex inside",
      "isotopy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4886G"
    }
  }
}