{
  "id": "1204.5924",
  "version": "v2",
  "published": "2012-04-26T13:52:35.000Z",
  "updated": "2012-12-21T16:10:46.000Z",
  "title": "The Topology of Parabolic Character Varieties of Free Groups",
  "authors": [
    "Indranil Biswas",
    "Carlos Florentino",
    "Sean Lawton",
    "Marina Logares"
  ],
  "comment": "16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicata",
  "journal": "Geometriae Dedicata, February 2014, Volume 168, Issue 1, pp 143-159",
  "doi": "10.1007/s10711-012-9822-1",
  "categories": [
    "math.AG",
    "math.GT",
    "math.RT"
  ],
  "abstract": "Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-21T16:10:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "20E05",
      "14P25",
      "14L17"
    ],
    "keywords": [
      "free group",
      "parabolic character varieties",
      "complex affine algebraic reductive group",
      "maximal compact subgroup",
      "strong deformation retraction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5924B"
    }
  }
}