{
  "id": "1301.7080",
  "version": "v2",
  "published": "2013-01-29T21:26:40.000Z",
  "updated": "2014-09-07T13:34:47.000Z",
  "title": "Ideal Whitehead Graphs in Out(F_r) III: Achieved Graphs in Rank 3",
  "authors": [
    "Catherine Pfaff"
  ],
  "comment": "Rewritten to improve readability. Typos fixed",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie determined a Teichm\\\"uller flow invariant stratification of the space of quadratic differentials. In this final paper of a three-paper series, we give a first step to an $Out(F_r)$ analog of the Masur-Smillie theorem. Since the ideal Whitehead graphs defined by Handel and Mosher give a strictly finer invariant in the analogous $Out(F_r)$ setting, we determine which of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible outer automorphisms in $Out(F_3)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-29T21:26:40.000Z",
      "abstract": "By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov, Masur and Smillie, in [MS93], determined a Teichmueller flow invariant stratification of the space of quadratic differentials. In this final paper of a three-paper series, we give a first step to an Out(F_r) analog of the [MS93] theorem. Since the ideal Whitehead graphs of [HM11] give a strictly finer invariant in the analogous Out(F_r) setting of a fully irreducible outer automorphism, we determined which of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible outer automorphisms in Out(F_3). It can be noted that our methods are valid in any rank.",
      "comment": "arXiv admin note: text overlap with arXiv:1205.5320",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-07T13:34:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "ideal whitehead graphs",
      "achieved graphs",
      "fully irreducible outer automorphism",
      "singularity index lists arise",
      "teichmueller flow invariant stratification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7080P"
    }
  }
}