A few remarks about symplectic filling

Eliashberg, Yakov¹

¹ Department of Mathematics, Stanford University, Stanford, California 94305-2125, USA

Geometry & topology, Tome 8 (2004) no. 1, pp. 277-293.

Résumé

We show that any compact symplectic manifold $\left(W,\omega \right)$ with boundary embeds as a domain into a closed symplectic manifold, provided that there exists a contact plane $\xi$ on $\partial W$ which is weakly compatible with $\omega$, i.e. the restriction $\omega$ | $\xi$ 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.

Détail

DOI : 10.2140/gt.2004.8.277

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

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