Volume 8, issue 1 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A few remarks about symplectic filling

Yakov Eliashberg

Geometry & Topology 8 (2004) 277–293

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 2000
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