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.
Notes on file formats
John B Etnyre
Department of Mathematics, University of Pennsylvania
209 South 33rd St, Philadelphia, PA 19104-6395, USA
Email: etnyre@math.upenn.edu
URL: http://math.upenn.edu/etnyre
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