{
  "id": "math/0112190",
  "version": "v1",
  "published": "2001-12-18T21:59:52.000Z",
  "updated": "2001-12-18T21:59:52.000Z",
  "title": "Geometry for palindromic automorphism groups of free groups",
  "authors": [
    "Henry H Glover",
    "Craig A. Jensen"
  ],
  "journal": "Comment. Math. Helv. 75 (2000) 644-667",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "We examine the palindromic automorphism group $\\Pi A(F_n)$ of a free group $F_n$, a group first defined by Collins which is related to hyperelliptic involutions of mapping class groups, congruence subgroups of $SL_n(\\Z)$, and symmetric automorphism groups of free groups. Cohomological properties of the group are explored by looking at a contractible space on which $\\Pi A(F_n)$ acts properly with finite quotient. Our results answer some conjectures of Collins and provide a few striking results about the cohomology of $\\Pi A(F_n)$, such as that its rational cohomology is zero at the vcd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-12-18T21:59:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F32",
      "20J05",
      "20F28",
      "55N91"
    ],
    "keywords": [
      "palindromic automorphism group",
      "free group",
      "symmetric automorphism groups",
      "hyperelliptic involutions",
      "rational cohomology"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12190G"
    }
  }
}