{
  "id": "0811.0799",
  "version": "v3",
  "published": "2008-11-05T19:47:19.000Z",
  "updated": "2012-03-23T01:46:45.000Z",
  "title": "Grid graphs and lattice surfaces",
  "authors": [
    "W. Patrick Hooper"
  ],
  "comment": "This version includes a more detailed description of how to derive algebraic formulas for the surfaces using the Schwarz-Christoffel Mapping Theorem. There were other minor improvements as well. 29 pages, 8 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "First, we apply Thurston's construction of pseudo-Anosov homeomorphisms to grid graphs and obtain translation surfaces whose Veech groups are commensurable to $(m,n,\\infty)$ triangle groups. These surfaces were first discovered by Bouw and M\\\"oller, however our treatment of the surfaces differs. We construct these surfaces by gluing together polygons in two ways. We use these elementary descriptions to compute the Veech groups, resolve primitivity questions, and describe the surfaces algebraically. Second, we show that some $(m,n, \\infty)$ triangle groups can not arise as Veech groups. This generalizes work of Hubert and Schmidt.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-03-23T01:46:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D50",
      "30F60"
    ],
    "keywords": [
      "grid graphs",
      "lattice surfaces",
      "veech groups",
      "triangle groups",
      "resolve primitivity questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0799H"
    }
  }
}