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15 February 2010 Strongly fillable contact manifolds and J-holomorphic foliations
Chris Wendl
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Duke Math. J. 151(3): 337-384 (15 February 2010). DOI: 10.1215/00127094-2010-001

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 T3 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 T3 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*T2 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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Chris Wendl. "Strongly fillable contact manifolds and J-holomorphic foliations." Duke Math. J. 151 (3) 337 - 384, 15 February 2010. https://doi.org/10.1215/00127094-2010-001

Information

Published: 15 February 2010
First available in Project Euclid: 8 February 2010

zbMATH: 1207.32022
MathSciNet: MR2605865
Digital Object Identifier: 10.1215/00127094-2010-001

Subjects:
Primary: 32Q65
Secondary: 57R17

Rights: Copyright © 2010 Duke University Press

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Vol.151 • No. 3 • 15 February 2010
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