{
  "id": "math/0401257",
  "version": "v2",
  "published": "2004-01-20T16:47:28.000Z",
  "updated": "2005-06-14T16:43:12.000Z",
  "title": "Is the deformation space of complete affine structures on the 2-torus smooth?",
  "authors": [
    "Oliver Baues",
    "William M. Goldman"
  ],
  "comment": "26 pages, 9 figures",
  "journal": "Contemporary Mathematics, Volume 389, 2005, p. 69 -89",
  "categories": [
    "math.DG"
  ],
  "abstract": "Periods of parallel exterior forms define natural coordinates on the deformation space of complete affine structures on the two-torus. These coordinates define a differentiable structure on this deformation space, under which it is diffeomorphic to $R^2$. The action of the mapping class group of $T^2$ is equivalent in these coordinates with the standard linear action of $\\SL_2(Z)$ on $R^2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-14T16:43:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D29",
      "22E40",
      "22F30",
      "57S30"
    ],
    "keywords": [
      "complete affine structures",
      "deformation space",
      "parallel exterior forms define natural",
      "exterior forms define natural coordinates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1257B"
    }
  }
}