{
  "id": "1105.0835",
  "version": "v2",
  "published": "2011-05-04T14:20:55.000Z",
  "updated": "2012-05-24T15:20:46.000Z",
  "title": "Tiling Spaces, Codimension One Attractors and Shape",
  "authors": [
    "Alex Clark",
    "John Hunton"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that any codimension one hyperbolic attractor of a di?eomorphism of a (d+1)-dimensional closed manifold is shape equivalent to a (d+1)-dimensional torus with a ?nite number of points removed, or, in the non-orientable case, to a space with a 2 to 1 covering by such a torus-less-points. Furthermore, we show that each orientable attractor is homeomorphic to a tiling space associated to an aperiodic tiling of Rd, but that the converse is generally not true. This work allows the de?nition of a new invariant for aperiodic tilings, in many cases ?ner than the cohomological or K-theoretic invariants studied to date.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-24T15:20:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tiling space",
      "codimension",
      "aperiodic tiling",
      "k-theoretic invariants",
      "shape equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.0835C"
    }
  }
}