On symplectic fillings

Abstract

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic manifold. We also relate properties of the open book decomposition of a contact manifold to its possible fillings. These results are also useful in proving property P for knots [P Kronheimer and T Mrowka, Geometry and Topology, 8 (2004) 295-310, math.GT/0311489] and in showing the contact Heegaard Floer invariant of a fillable contact structure does not vanish [P Ozsvath and Z Szabo, Geometry and Topology, 8 (2004) 311-334, math.GT/0311496].

Published electronically at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-5.abs.html

References in corpus (3)

• Holomorphic disks and genus bounds
• Witten's conjecture and Property P
• An infinite family of tight, not semi-fillable contact three-manifolds

Cited by in corpus (12)

• Holomorphic disks and genus bounds
• Knot Floer homology and rational surgeries
• Witten's conjecture and Property P
• Khovanov module and the detection of unlinks
• Four-dimensional symplectic cobordisms containing three-handles
• Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology
• Orbit equivalences of $\mathbb{R}$-covered Anosov flows and hyperbolic-like actions on the line
• A note on knot Floer homology of links
• Contact surgery and symplectic caps
• Planarity in higher-dimensional contact manifolds
• Taut foliations leafwise branch cover S^2
• Symplectic fillings of unit cotangent bundles of hyperbolic surfaces