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A few remarks about symplectic filling

Yakov Eliashberg
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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 ξon dW which is weakly compatible with omega, i.e. the restriction ω|ξdoes not vanish and the contact orientation of dW and its orientation as the boundary of the symplectic manifold W coincide. This result provides a useful tool for new applications by Ozsvath-Szabo 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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Yakov Eliashberg. 2004-02-27. A few remarks about symplectic filling. https://arxiv.org/abs/math/0311459

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