{
  "id": "1010.4753",
  "version": "v2",
  "published": "2010-10-22T16:39:23.000Z",
  "updated": "2011-04-20T16:29:15.000Z",
  "title": "Relative outer automorphisms of free groups",
  "authors": [
    "Erika Meucci"
  ],
  "comment": "24 pages, 16 figures, corrected typos, revised argument in section 5, results unchanged",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let $A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative automorphisms $Aut(F_n;A_1,...,A_k)$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The group of relative outer automorphisms is defined as $Out(F_n;A_1,...,A_k) = Aut(F_n;A_1,...,A_k)/Inn(F_n)$, where $Inn(F_n)$ is the normal subgroup of $Aut(F_n)$ given by all the inner automorphisms. We define a contractible space on which $Out(F_n;A_1,...,A_k)$ acts with finite stabilizers and we compute the virtual cohomological dimension of this group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-20T16:29:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relative outer automorphisms",
      "free groups",
      "virtual cohomological dimension",
      "normal subgroup",
      "inner automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4753M"
    }
  }
}