{
  "id": "math/9912145",
  "version": "v2",
  "published": "1999-12-17T21:25:39.000Z",
  "updated": "2001-05-25T08:34:36.000Z",
  "title": "Symplectic 2-handles and transverse links",
  "authors": [
    "David T. Gay"
  ],
  "comment": "22 pages, 5 figures, AMS-Latex. Accepted for publication in the Transactions of the American Mathematical Society. Current version is identical to the final version submitted to Transactions, using amsart document class. Abstract slightly expanded",
  "categories": [
    "math.GT",
    "math.DG",
    "math.SG"
  ],
  "abstract": "A standard convexity condition on the boundary of a symplectic manifold involves an induced positive contact form (and contact structure) on the boundary; the corresponding concavity condition involves an induced negative contact form. We present two methods of symplectically attaching 2-handles to convex boundaries of symplectic 4-manifolds along links transverse to the induced contact structures. One method results in concave boundaries and depends on a fibration of the link complement over S^1; in this case the handles can be attached with any framing larger than a lower bound determined by the fibration. The other method results in a weaker convexity condition on the new boundary (sufficient to imply tightness of the new contact structure), and in this case the handles can be attached with any framing less than a certain upper bound. These methods supplement methods developed by Weinstein and Eliashberg for attaching symplectic 2-handles along Legendrian knots.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-05-25T08:34:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17",
      "57R65",
      "57M99"
    ],
    "keywords": [
      "transverse links",
      "symplectic",
      "contact structure",
      "method results",
      "standard convexity condition"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12145G"
    }
  }
}