Duke Mathematical Journal
- Duke Math. J.
- Volume 151, Number 3 (2010), 337-384.
Strongly fillable contact manifolds and -holomorphic foliations
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 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 are equivalent up to symplectic deformation and blowup. These constructions result from a compactness theorem for punctured -holomorphic curves that foliate a convex symplectic manifold. We use it also to show that the compactly supported symplectomorphism group on 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
Duke Math. J., Volume 151, Number 3 (2010), 337-384.
First available in Project Euclid: 8 February 2010
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Wendl, Chris. Strongly fillable contact manifolds and $J$ -holomorphic foliations. Duke Math. J. 151 (2010), no. 3, 337--384. doi:10.1215/00127094-2010-001. https://projecteuclid.org/euclid.dmj/1265637657