{
  "id": "1705.03206",
  "version": "v1",
  "published": "2017-05-09T07:12:44.000Z",
  "updated": "2017-05-09T07:12:44.000Z",
  "title": "Fibered commensurability on $\\mathrm{Out}(F_{n})$",
  "authors": [
    "Hidetoshi Masai",
    "Ryosuke Mineyama"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We define and discuss fibered commensurability of outer automorphisms of the free groups, which lets us study symmetries of outer automorphisms. The notion of fibered commensurability is first defined by Calegari-Sun-Wang on mapping class groups. The Nielsen-Thurston type of mapping classes is a commensurability invariant. One of the important facts of fibered commensurability on mapping class groups is for the case of pseudo-Anosovs, there is a unique minimal element in each fibered commensurability class. In this paper, we first show that being ageometric and fully irreducible is a commensurability invariant. Then for such outer automorphisms, we prove that there is a unique minimal element in each fibered commensurability class, under asymmetry assumption on the ideal Whitehead graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-09T07:12:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "outer automorphisms",
      "unique minimal element",
      "fibered commensurability class",
      "mapping class groups",
      "commensurability invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}