{
  "id": "1605.05659",
  "version": "v1",
  "published": "2016-05-17T13:19:36.000Z",
  "updated": "2016-05-17T13:19:36.000Z",
  "title": "Cutting sequences on square-tiled surfaces",
  "authors": [
    "Charles C. Johnson"
  ],
  "comment": "23 pages, 9 figures",
  "categories": [
    "math.DS",
    "math.MG"
  ],
  "abstract": "We characterize cutting sequences of infinite geodesics on square-tiled surfaces by considering interval exchanges on specially chosen intervals on the surface. These interval exchanges can be thought of as skew products over a rotation, and we convert cutting sequences to symbolic trajectories of these interval exchanges to show that special types of combinatorial lifts of Sturmian sequences completely describe all cutting sequences on a square-tiled surface. Our results extend the list of families of surfaces where cutting sequences are understood to a dense subset of the moduli space of all translation surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-17T13:19:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E35"
    ],
    "keywords": [
      "square-tiled surface",
      "considering interval exchanges",
      "moduli space",
      "dense subset",
      "infinite geodesics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}