{
  "id": "math/0307115",
  "version": "v2",
  "published": "2003-07-09T17:07:21.000Z",
  "updated": "2003-11-28T08:27:17.000Z",
  "title": "Koszul duality and equivariant cohomology",
  "authors": [
    "Matthias Franz"
  ],
  "comment": "12 pages. v2: proof of Theorem 1.2 modified in Sec. 6, references added, other minor changes",
  "journal": "Documenta Math. 11 (2006), 243-259",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let G be a topological group such that its homology H(G) with coefficients in a principal ideal domain R is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between G-spaces and spaces over BG to the Koszul duality between modules up to homotopy over H(G) and H^*(BG). This gives in particular a Cartan-type model for the equivariant cohomology of a G-space. As another corollary, we obtain a multiplicative quasi-isomorphism C^*(BG) -> H^*(BG). A key step in the proof is to show that a differential Hopf algebra is formal in the category of A-infinity algebras provided that it is free over R and its homology an exterior algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-11-28T08:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S37",
      "55N91",
      "16E45",
      "55N10"
    ],
    "keywords": [
      "equivariant cohomology",
      "koszul duality",
      "singular cochain functor carries",
      "exterior algebra",
      "differential hopf algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7115F"
    }
  }
}