{
  "id": "0907.4642",
  "version": "v4",
  "published": "2009-07-27T14:34:01.000Z",
  "updated": "2014-03-05T15:11:13.000Z",
  "title": "A combinatorial proof of the Degree Theorem in Auter space",
  "authors": [
    "Robert McEwen",
    "Matthew C. B. Zaremsky"
  ],
  "comment": "Final version, in New York J. Math. (http://nyjm.albany.edu/j/2014/20-13.html). Minor changes from v3. 12 pages, 2 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We use discrete Morse theory to give a new proof of the Degree Theorem in Auter space A_n. There is a filtration of A_n into subspaces A_{n,k} using the degree of a graph, and the Degree Theorem says that each A_{n,k} is (k-1)-connected. This result is useful, for example to calculate stability bounds for the homology of Aut(F_n). The standard proof of the Degree Theorem is global in nature. Here we give a proof that only uses local considerations, and lends itself more readily to generalization.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-03-05T15:11:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M07",
      "20F28"
    ],
    "keywords": [
      "auter space",
      "combinatorial proof",
      "degree theorem says",
      "discrete morse theory",
      "stability bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.4642M"
    }
  }
}