{
  "id": "1012.1433",
  "version": "v1",
  "published": "2010-12-07T08:57:28.000Z",
  "updated": "2010-12-07T08:57:28.000Z",
  "title": "The stable cohomology of automorphisms of free groups with coefficients in the homology representation",
  "authors": [
    "Oscar Randal-Williams"
  ],
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "We study the cohomology of Aut(F_n) and Out(F_n) with coefficients in the modules \\wedge^q H, \\wedge H^*, Sym^q H or Sym^q H^*, where H is the Out(F_n)-module obtained by abelianising the free group F_n. For reasons which are not conceptually clear, taking coefficients in H and its related modules behaves in a far less trivial way than taking coefficients in H^* and its related modules. Based on a conjectural homology stability theorem for spaces of graphs labeled by a simply connected background space, we give a stable integral calculation of these groups in low degrees, and modulo a further conjecture a stable rational calculation in all degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-07T08:57:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F28",
      "20J06",
      "57R20"
    ],
    "keywords": [
      "free group",
      "homology representation",
      "coefficients",
      "stable cohomology",
      "conjectural homology stability theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.1433R"
    }
  }
}