Volume 8 (2004)

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A few remarks about symplectic filling

Yakov Eliashberg

Geometry & Topology 8 (2004) 277–293

DOI: 10.2140/gt.2004.8.277

arXiv: math.SG/0308183

Abstract

We show that any compact symplectic manifold (W,ω) with boundary embeds as a domain into a closed symplectic manifold, provided that there exists a contact plane ξ on ∂W which is weakly compatible with ω, i.e. the restriction ω|ξ does not vanish and the contact orientation of ∂W and its orientation as the boundary of the symplectic manifold W coincide. This result provides a useful tool for new applications by Ozsváth–Szabó of Seiberg–Witten Floer homology theories in three-dimensional topology and has helped complete the Kronheimer–Mrowka proof of Property P for knots.

To Ada

Keywords

contact manifold, symplectic filling, symplectic Lefschetz fibration, open book decomposition

Mathematical Subject Classification

Primary: 53C15

Secondary: 57M50

References
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Publication

Received: 25 November 2003
Revised: 13 January 2004
Accepted: 2 January 2004
Published: 14 February 2004
Proposed: Leonid Polterovich
Seconded: Peter Ozsváth, Dieter Kotschick

Authors
Yakov Eliashberg
Department of Mathematics
Stanford University
Stanford
California 94305-2125
USA