{
  "id": "1301.6645",
  "version": "v2",
  "published": "2013-01-28T19:06:38.000Z",
  "updated": "2014-09-07T16:18:41.000Z",
  "title": "Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank",
  "authors": [
    "Catherine Pfaff"
  ],
  "comment": "The main revisions are to fill in missing conditions on rotationlessness. In particular, a power should have been taken of the map giving the main theorem. However, Remark 4.3 also needed to be adjusted. There was also a confusing typo in the ideal decomposition proposition that needed to be fixed",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show how to construct, for each $r \\geq 3$, an ageometric, fully irreducible $\\phi\\in Out(F_r)$ whose ideal Whitehead graph is the complete graph on $2r-1$ vertices. This paper is the second in a series of three where we show that precisely eighteen of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible $\\phi \\in Out(F_3)$. The result is a first step to an $Out(F_r)$ version of the Masur-Smillie theorem proving precisely which index lists arise from singular measured foliations for pseudo-Anosov mapping classes. In this paper we additionally give a method for finding periodic Nielsen paths and prove a criterion for identifying representatives of ageometric, fully irreducible $\\phi\\in Out(F_r)$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-28T19:06:38.000Z",
      "abstract": "We show how to construct, for each r > 2, an ageometric, fully irreducible outer automorphism in Out(F_r) whose ideal Whitehead graph is the complete graph on 2r-1 vertices. This paper is the second in a series of three where we show that precisely eighteen of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible outer automorphism in Out(F_3). The result is a first step to an Out(F_r) version of the Masur-Smillie theorem proving precisely which index lists arise from singular measured foliations for pseudo-Anosov mapping classes. In this paper we additionally give a method for finding periodic Nielsen paths and prove a criterion for identifying representatives of ageometric, fully irreducible outer automorphism in Out(F_r).",
      "comment": "arXiv admin note: text overlap with arXiv:1205.5320",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-07T16:18:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "ideal whitehead graph",
      "complete graph",
      "fully irreducible outer automorphism",
      "index lists arise",
      "finding periodic nielsen paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.6645P"
    }
  }
}