{
  "id": "math/0607069",
  "version": "v4",
  "published": "2006-07-03T21:27:29.000Z",
  "updated": "2009-06-09T15:03:15.000Z",
  "title": "Torsion and abelianization in equivariant cohomology",
  "authors": [
    "Tara Holm",
    "Reyer Sjamaar"
  ],
  "comment": "30 pages. References added and typos corrected",
  "journal": "Transform. Groups 13 (2008), no. 3-4, 585-615",
  "categories": [
    "math.AT",
    "math.AG",
    "math.SG"
  ],
  "abstract": "Let $X$ be a topological space upon which a compact connected Lie group $G$ acts. It is well-known that the equivariant cohomology $H_G^*(X;\\Q)$ is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology $H_T^*(X;\\Q)$, where $T$ is a maximal torus of $G$. This relationship breaks down for coefficient rings $\\k$ other than $\\Q$. Instead, we prove that under a mild condition on $\\k$ the algebra $H_G^*(X,\\k)$ is isomorphic to the subalgebra of $H_T^*(X,\\k)$ annihilated by the divided difference operators.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-06-09T15:03:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N91"
    ],
    "keywords": [
      "equivariant cohomology",
      "abelianization",
      "weyl group invariants",
      "compact connected lie group",
      "maximal torus"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7069H"
    }
  }
}