{
  "id": "1506.04536",
  "version": "v1",
  "published": "2015-06-15T09:55:44.000Z",
  "updated": "2015-06-15T09:55:44.000Z",
  "title": "Free group automorphisms, Train tracks, Index realization, Gate structure",
  "authors": [
    "Thierry Coulbois",
    "Martin Lustig"
  ],
  "comment": "19 pages, 3 figures, 1 table",
  "categories": [
    "math.GR"
  ],
  "abstract": "For any surface $\\Sigma$ of genus $g \\geq 1$ and (essentially) any collection of positive integers $i_1, i_2, \\ldots, i_\\ell$ with $i_1+\\cdots +i_\\ell = 4g-4$ Masur and Smillie have shown that there exists a pseudo-Anosov homeomorphism $h:\\Sigma \\to \\Sigma$ with precisely $\\ell$ singularities $S_1, \\ldots, S_\\ell$ in its stable foliation $\\cal L$, such that $\\cal L$ has precisely $i_k+2$ separatrices raying out from each $S_k$. In this paper we prove the analogue of this result for automorphisms of a free group $F_N$, where \"pseudo-Anosov homeomorphism\" is replaced by \"fully irreducible automorphism\" and the Gauss-Bonnet equality $i_1+\\cdots +i_\\ell = 4g-4$ is replaced by the index inequality $i_1+\\cdots +i_\\ell \\leq 2N-2$ from Gaboriau, Jaeger, Levitt and Lustig.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-15T09:55:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "20E08",
      "20F65",
      "57R30"
    ],
    "keywords": [
      "free group automorphisms",
      "gate structure",
      "train tracks",
      "index realization",
      "pseudo-anosov homeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150604536C"
    }
  }
}