On symplectic fillings

Details On symplectic fillings On symplectic fillings

2003-12-03

arxiv.org/abs/math/0312091v2

Algebraic and Geometric Topology 4 (2004) 73-80

Mathematics

Symplectic Geometry

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

Scientific paper

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].

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