{
  "id": "1405.3580",
  "version": "v2",
  "published": "2014-05-14T17:27:56.000Z",
  "updated": "2015-01-20T17:23:05.000Z",
  "title": "Fundamental Group of Moduli Spaces of Representations",
  "authors": [
    "Indranil Biswas",
    "Sean Lawton"
  ],
  "comment": "9 pages, to appear in Geometriae Dedicata",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "Let S be a surface of genus g with n points removed, G a connected Lie group, and X(G) the moduli space of representations of the fundamental group of S into G. We compute the fundamental group of X(G) when n>0 and G is a real or complex reductive algebraic group, or a compact Lie group; and when n=0 and G=GL(m,C), SL(m,C), U(m), or SU(m).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-14T17:27:56.000Z",
      "abstract": "Let S be a surface of genus g with n points removed, G a connected Lie group, and X(G) the moduli space of representations of the fundamental group of S into G. We compute the fundamental group of X(G) when n>0 and G is a real or complex reductive algebraic group, or a compact Lie group; and when n=0 and G=GL(n,C), SL(n,C), U(n), or SU(n).",
      "comment": "8 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-20T17:23:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14L30",
      "14F35"
    ],
    "keywords": [
      "fundamental group",
      "moduli space",
      "representations",
      "complex reductive algebraic group",
      "compact lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.3580B"
    }
  }
}