{
  "id": "0911.1417",
  "version": "v4",
  "published": "2009-11-07T13:56:58.000Z",
  "updated": "2010-05-04T23:23:01.000Z",
  "title": "On a spectral sequence for twisted cohomologies",
  "authors": [
    "Weiping Li",
    "Xiugui Liu",
    "He Wang"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let ($\\Omega^{\\ast}(M), d$) be the de Rham cochain complex for a smooth compact closed manifolds $M$ of dimension $n$. For an odd-degree closed form $H$, there are a twisted de Rham cochain complex $(\\Omega^{\\ast}(M), d+H_\\wedge)$ and its associated twisted de Rham cohomology $H^*(M,H)$. We show that there exists a spectral sequence $\\{E^{p, q}_r, d_r\\}$ derived from the filtration $F_p(\\Omega^{\\ast}(M))=\\bigoplus_{i\\geq p}\\Omega^i(M)$ of $\\Omega^{\\ast}(M)$, which converges to the twisted de Rham cohomology $H^*(M,H)$. We also show that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-05-04T23:23:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J52",
      "57Q10",
      "58J40",
      "81T30"
    ],
    "keywords": [
      "spectral sequence",
      "twisted cohomologies",
      "rham cochain complex",
      "rham cohomology",
      "smooth compact closed manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.1417L"
    }
  }
}