{
  "id": "1103.1624",
  "version": "v2",
  "published": "2011-03-08T20:47:01.000Z",
  "updated": "2012-11-01T09:59:35.000Z",
  "title": "Outer automorphism groups of free groups: linear and free representations",
  "authors": [
    "Dawid Kielak"
  ],
  "comment": "Final version. To appear in JLMS",
  "doi": "10.1112/jlms/jds077",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study the existence of homomorphisms between Out(F_n) and Out(F_m) for n > 5 and m < n(n-1)/2, and conclude that if m is not equal to n then each such homomorphism factors through the finite group of order 2. In particular this provides an answer to a question of Bogopol'skii and Puga. In the course of the argument linear representations of Out(F_n) in dimension less than n(n+1)/2 over fields of characteristic zero are completely classified. It is shown that each such representation has to factor through the natural projection from Out(F_n) to GL(n,Z) coming from the action of Out(F_n) on the abelianisation of F_n. We obtain similar results about linear representation theory of Out(F_4) and Out(F_5).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-01T09:59:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F28",
      "57M60",
      "20C15"
    ],
    "keywords": [
      "outer automorphism groups",
      "free groups",
      "free representations",
      "argument linear representations",
      "linear representation theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1624K"
    }
  }
}