{
  "id": "math/9907041",
  "version": "v2",
  "published": "1999-07-07T13:47:29.000Z",
  "updated": "1999-07-27T11:38:34.000Z",
  "title": "Simple curves on surfaces",
  "authors": [
    "Igor Rivin"
  ],
  "comment": "16 pages, many figures",
  "categories": [
    "math.GT",
    "math.DG",
    "math.GR"
  ],
  "abstract": "We show that the number of simple closed geodesics of length bounded by L on a hyperbolic surface of genus g with c cusps and b boundary components grows roughly like L^{6g+2b+2c-6}. This has been conjectured for some time.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-07-27T11:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "34C25"
    ],
    "keywords": [
      "simple curves",
      "simple closed geodesics",
      "hyperbolic surface",
      "boundary components grows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7041R"
    }
  }
}