{
  "id": "0904.4177",
  "version": "v1",
  "published": "2009-04-27T14:47:49.000Z",
  "updated": "2009-04-27T14:47:49.000Z",
  "title": "Cohomology of preimages with local coefficients",
  "authors": [
    "Daciberg Lima Goncalves",
    "Peter Wong"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 4 October 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 1471-1489",
  "doi": "10.2140/agt.2006.6.1471",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let M,N and B\\subset N be compact smooth manifolds of dimensions n+k,n and \\ell, respectively. Given a map f from M to N, we give homological conditions under which g^{-1}(B) has nontrivial cohomology (with local coefficients) for any map g homotopic to f. We also show that a certain cohomology class in H^j(N,N-B) is Poincare dual (with local coefficients) under f^* to the image of a corresponding class in H_{n+k-j}(f^{-1}(B)) when f is transverse to B. This generalizes a similar formula of D Gottlieb in the case of simple coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-27T14:47:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M20",
      "55S35"
    ],
    "keywords": [
      "local coefficients",
      "compact smooth manifolds",
      "simple coefficients",
      "poincare dual",
      "cohomology class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.4177L"
    }
  }
}