Symplectic $2$-handles and transverse links
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- by David T. Gay PDF
- Trans. Amer. Math. Soc. 354 (2002), 1027-1047 Request permission
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.References
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Additional Information
- David T. Gay
- Affiliation: Department of Mathematics, University of Arizona, 617 North Santa Rita, Post Office Box 210089, Tucson, Arizona 85721
- MR Author ID: 686652
- Email: dtgay@math.arizona.edu
- Received by editor(s): January 24, 2000
- Received by editor(s) in revised form: June 4, 2001
- Published electronically: October 11, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 1027-1047
- MSC (2000): Primary 57R17, 57R65; Secondary 57M99
- DOI: https://doi.org/10.1090/S0002-9947-01-02890-2
- MathSciNet review: 1867371