On symplectic fillings

Etnyre, John B

doi:10.2140/agt.2004.4.73

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On symplectic fillings

John B Etnyre

Algebraic & Geometric Topology 4 (2004) 73–80

DOI: 10.2140/agt.2004.4.73

arXiv: math.SG/0312091

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

Mathematical Subject Classification 2000

Primary: 53D05, 53D10

Secondary: 57M50

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Publication

Received: 7 January 2004

Accepted: 19 January 2004

Published: 14 February 2004

Authors

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

Volume 4, issue 1 (2004)