{
  "id": "math/0403146",
  "version": "v1",
  "published": "2004-03-09T17:01:48.000Z",
  "updated": "2004-03-09T17:01:48.000Z",
  "title": "A Homotopy Theory for Graphs",
  "authors": [
    "E. Babson",
    "H. Barcelo",
    "M. de Longueville",
    "R. Laubenbacher"
  ],
  "comment": "11 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the given graph. We present a natural candidate for such a cell complex, together with a homomorphism between the corresponding groups that indeed yields an isomorphism, if a cubical analog of the simplicial approximation theorem holds, which - so far - we were unable to prove.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-09T17:01:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C99",
      "55Q99"
    ],
    "keywords": [
      "homotopy theory",
      "a-homotopy groups",
      "simplicial approximation theorem holds",
      "infinite cell complex",
      "natural candidate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3146B"
    }
  }
}