{
  "id": "0802.0919",
  "version": "v1",
  "published": "2008-02-07T08:07:02.000Z",
  "updated": "2008-02-07T08:07:02.000Z",
  "title": "Finiteness results for flat surfaces: large cusps and short geodesics",
  "authors": [
    "John Smillie",
    "Barak Weiss"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For fixed g and T we show that finiteness of the set of affine equivalence classes of flat surfaces of genus g whose Veech groups contain a cusp of hyperbolic co-area less than T. We obtain new restrictions on Veech groups: we show that any non-elementary Veech group can appear only finitely many times in a fixed stratum, that any non-elementary Veech group is of finite index in its normalizer, and that the quotient of the upper half plane by a non-lattice Veech group contains arbitrarily large embedded disks. These are proved using the finiteness of the set of affine equivalence classes of flat surfaces of genus g whose Veech group contains a hyperbolic element with eigenvalue less than T.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-07T08:07:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flat surfaces",
      "short geodesics",
      "large cusps",
      "finiteness results",
      "group contains arbitrarily large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0919S"
    }
  }
}