{
  "id": "math/0207169",
  "version": "v2",
  "published": "2002-07-19T19:39:37.000Z",
  "updated": "2003-08-05T21:18:20.000Z",
  "title": "Hodge cohomology of gravitational instantons",
  "authors": [
    "Tamas Hausel",
    "Eugenie Hunsicker",
    "Rafe Mazzeo"
  ],
  "comment": "45 pages; corrected final version. To appear in Duke Math. Journal",
  "categories": [
    "math.DG",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the space of L^2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincar\\'e metrics on Q-rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in K\\\"ahler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L^2 signature formula implied by our result is closely related to the one proved by Dai [dai] and more generally by Vaillant [Va], and identifies Dai's tau invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron [Car] and the forthcoming paper of Cheeger and Dai [CD]. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L^2 harmonic forms in duality theories in string theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-08-05T21:18:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A14",
      "32S60"
    ],
    "keywords": [
      "gravitational instantons",
      "hodge cohomology",
      "harmonic forms",
      "intersection cohomology",
      "identifies dais tau invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 590952,
      "adsabs": "2002math......7169H"
    }
  }
}