Algebraic & Geometric Topology

On symplectic fillings

John B Etnyre

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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].

Article information

Algebr. Geom. Topol., Volume 4, Number 1 (2004), 73-80.

Received: 7 January 2004
Accepted: 19 January 2004
First available in Project Euclid: 21 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D05: Symplectic manifolds, general 53D10: Contact manifolds, general
Secondary: 57M50: Geometric structures on low-dimensional manifolds

tight symplectic filling convexity


Etnyre, John B. On symplectic fillings. Algebr. Geom. Topol. 4 (2004), no. 1, 73--80. doi:10.2140/agt.2004.4.73.

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