{
  "id": "1311.4490",
  "version": "v2",
  "published": "2013-11-18T18:50:36.000Z",
  "updated": "2014-09-07T14:14:49.000Z",
  "title": "$Out(F_3)$ Index Realization",
  "authors": [
    "Catherine Pfaff"
  ],
  "comment": "Readability improved & paper expanded to include more background on how the examples can be verified",
  "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 Teichmueller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem for $Out(F_3)$. That is, we determine which index lists permitted by the Gaboriau-Jaeger-Levitt-Lustig index sum inequality are achieved by fully irreducible outer automorphisms of the rank-$3$ free group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-18T18:50:36.000Z",
      "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\\\"{u}ller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem for $Out(F_3)$. That is, we determine in rank $3$ which index lists permitted by the index sum inequality of Gaboriau, \\\"aeger, Levitt, and Lustig are achieved by fully irreducible outer automorphisms of the rank-$3$ free group.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-07T14:14:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "index realization",
      "singularity index lists arise",
      "index sum inequality",
      "flow invariant stratification",
      "pseudo-anosov surface homeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4490P"
    }
  }
}