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Strongly fillable contact manifolds and $J$-holomorphic foliations
Chris Wendl
Source: Duke Math. J. Volume 151, Number 3
(2010), 337-384.
Abstract
We prove that every strong symplectic filling of a planar contact manifold admits a symplectic Lefschetz fibration over the disk, and every strong filling of $T^3$ similarly admits a Lefschetz fibration over the annulus. It follows that strongly fillable planar contact structures are also Stein fillable, and all strong fillings of $T^3$ are equivalent up to symplectic deformation and blowup. These constructions result from a compactness theorem for punctured $J$-holomorphic curves that foliate a convex symplectic manifold. We use it also to show that the compactly supported symplectomorphism group on $T^*T^2$ is contractible, and to define an obstruction to strong fillability that yields a non-gauge-theoretic proof of Gay's recent nonfillability result [G] for contact manifolds with positive Giroux torsion
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1265637657
Digital Object Identifier: doi:10.1215/00127094-2010-001
Zentralblatt MATH identifier: 05688243
Mathematical Reviews number (MathSciNet): MR2605865
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