A few remarks about symplectic filling

Eliashberg, Yakov

doi:10.2140/gt.2004.8.277

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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 $\partial W$ which is weakly compatible with $ω$ , i.e. the restriction $ω$ | $ξ$ does not vanish and the contact orientation of $\partial W$ 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.

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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

Volume 8, issue 1 (2004)