{
  "id": "math/0306341",
  "version": "v3",
  "published": "2003-06-24T11:21:19.000Z",
  "updated": "2003-12-15T13:24:39.000Z",
  "title": "Kirwan map and moduli space of flat connections",
  "authors": [
    "Sebastien Racaniere"
  ],
  "comment": "15 pages, typos corrected, Section 3 rewritten to clarify presentation",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "If $K$ is a compact Lie group and $g\\geq 2$ an integer, the space $K^{2g}$ is endowed with the structure of a Hamiltonian space with a Lie group valued moment map $\\Phi$. Let $\\beta$ be in the centre of $K$. The reduction $\\Phi^{-1}(\\beta)/K$ is homeomorphic to a moduli space of flat connections. When $K$ is simply connected, a direct consequence of a recent paper of Bott, Tolman and Weitsman is to give a set of generators for the $K$-equivariant cohomology of $\\Phi^{-1}(\\beta)$. Another method to construct classes in $H^*_K(\\Phi^{-1}(\\beta))$ is by using the so called universal bundle. When the group is $\\Sun$ and $\\beta$ is a generator of the centre, these last classes are known to also generate the equivariant cohomology of $\\Phi^{-1}(\\beta)$. The aim of this paper is to compare the classes constructed using the result of Bott, Tolman and Weitsman and the ones using the universal bundle.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-12-15T13:24:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D20",
      "22E67"
    ],
    "keywords": [
      "moduli space",
      "flat connections",
      "kirwan map",
      "universal bundle",
      "lie group valued moment map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6341R"
    }
  }
}