{
  "id": "1107.5303",
  "version": "v3",
  "published": "2011-07-26T19:36:43.000Z",
  "updated": "2012-08-27T19:03:34.000Z",
  "title": "Hierarchy of graph matchbox manifolds",
  "authors": [
    "Olga Lukina"
  ],
  "comment": "New examples added at the end of Section 2; Introduction is rewritten. To appear in Topology and its Applications",
  "doi": "10.1016/j.topol.2012.08.011",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call its level. We develop the fusion construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is simple, it gives us a powerful tool to study graph foliated spaces. Using fusion, we prove that there is a hierarchy of graph foliated spaces at infinite levels. We also construct examples of graph foliated spaces with various dynamical and geometric properties.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-08-27T19:03:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "37B05",
      "54H20"
    ],
    "keywords": [
      "graph matchbox manifolds",
      "study graph foliated spaces",
      "construct examples",
      "infinite levels",
      "geometric properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5303L"
    }
  }
}