{
  "id": "math/0610761",
  "version": "v3",
  "published": "2006-10-25T17:57:26.000Z",
  "updated": "2007-02-19T19:34:58.000Z",
  "title": "Cohomology of the space of commuting n-tuples in a compact Lie group",
  "authors": [
    "Thomas Baird"
  ],
  "comment": "11 pages Changes made: Implemented referee recommendations, in particular to use the Vietoris mapping theorem to generalize results and simplify arguments",
  "journal": "Algebraic & Geometric Topology 7 (2007) 737-754",
  "categories": [
    "math.AT"
  ],
  "abstract": "Consider the space Hom(Z^n,G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of Hom(Z^n,G), which allows us to derive formulas for its ordinary and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the action of the Weyl group. This is an application of a general theorem concerning G-spaces for which every element is fixed by a maximal torus.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-02-19T19:34:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact lie group",
      "commuting n-tuples",
      "maximal torus",
      "general theorem concerning g-spaces",
      "real algebraic variety"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10761B"
    }
  }
}