{
  "id": "math/0210179",
  "version": "v1",
  "published": "2002-10-11T19:20:08.000Z",
  "updated": "2002-10-11T19:20:08.000Z",
  "title": "Tiling Spaces are Inverse Limits",
  "authors": [
    "Lorenzo Sadun"
  ],
  "comment": "Latex, 6 pages, including one embedded figure",
  "doi": "10.1063/1.1613041",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MG",
    "math.MP"
  ],
  "abstract": "Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space of tilings of M, with finite local complexity (relative to some symmetry group Gamma) and closed in the natural topology. Then Omega is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Gamma. This result extends previous results of Anderson and Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and of G\\\"ahler. In particular, the construction in this paper is a natural generalization of G\\\"ahler's.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-11T19:20:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B50",
      "52C23",
      "54F65",
      "37C85",
      "02.40.Pc"
    ],
    "keywords": [
      "inverse limit",
      "tiling spaces",
      "arbitrary riemannian homogeneous space",
      "compact finite-dimensional branched manifolds",
      "symmetry group gamma"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Mathematical Physics",
      "year": 2003,
      "month": "Nov",
      "volume": 44,
      "number": 11,
      "pages": 5410
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003JMP....44.5410S"
    }
  }
}