Algebraic and Geometric Topology 4 (2004), paper no. 5, pages 73-80.

On symplectic fillings

John B Etnyre

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] 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].

Keywords. Tight, symplectic filling, convexity

AMS subject classification. Primary: 53D05, 53D10. Secondary: 57M50.

DOI: 10.2140/agt.2004.4.73

E-print: arXiv:math.SG/0312091

Submitted: 7 January 2004. Accepted: 19 January 2004. Published: 14 February 2004.

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John B Etnyre
Department of Mathematics, University of Pennsylvania
209 South 33rd St, Philadelphia, PA 19104-6395, USA
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