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].
Cite
@article{arxiv.math/0312091,
title = {On symplectic fillings},
author = {John B Etnyre},
journal= {arXiv preprint arXiv:math/0312091},
year = {2014}
}
Comments
Published electronically at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-5.abs.html