Symplectic 2-handles and transverse links
Abstract
Description
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.
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
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