{
  "id": "math/0401186",
  "version": "v2",
  "published": "2004-01-15T17:25:34.000Z",
  "updated": "2004-05-20T19:36:10.000Z",
  "title": "Constructing symplectic forms on 4-manifolds which vanish on circles",
  "authors": [
    "David T. Gay",
    "Robion Kirby"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper20.abs.html",
  "journal": "Geom. Topol. 8(2004) 743-777",
  "categories": [
    "math.GT",
    "math.DG",
    "math.SG"
  ],
  "abstract": "Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha, which is symplectic on the complement of a finite set of unknotted circles. The number of circles, counted with sign, is given by d = (c_1(s)^2 -3sigma(X) -2chi(X))/4, where s is a certain spin^C structure naturally associated to w.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-05-20T19:36:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17",
      "57M50",
      "32Q60"
    ],
    "keywords": [
      "constructing symplectic forms",
      "poincare dual",
      "finite set",
      "unknotted circles",
      "complement"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1186G"
    }
  }
}