{
  "id": "1210.5762",
  "version": "v1",
  "published": "2012-10-21T20:50:24.000Z",
  "updated": "2012-10-21T20:50:24.000Z",
  "title": "Ideal Whitehead Graphs in Out(F_r) I: Some Unachieved Graphs",
  "authors": [
    "Catherine Pfaff"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1205.5320",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "H. Masur and J. Smillie proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher ask: Is each connected, simplicial, (2r-1)-vertex graph the ideal Whitehead graph of a fully irreducible outer automorphism in Out(F_r)? We answer this question in the negative by exhibiting, for each r, examples of connected (2r-1)-vertex graphs that are not the ideal Whitehead graph of any fully irreducible outer automorphism in Out(F_r)? In the course of our proof we also develop machinery used in \"Constructing and Classifying Fully Irreducible Outer Automorphisms of Free Groups\" to fully answer the question in the rank-three case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-21T20:50:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "F.6.5"
    ],
    "keywords": [
      "ideal whitehead graph",
      "fully irreducible outer automorphism",
      "unachieved graphs",
      "free groups",
      "singularity index lists arise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5762P"
    }
  }
}