Geometry & Topology, Vol. 8 (2004) Paper no. 6, pages 277--293.

A few remarks about symplectic filling

Yakov Eliashberg

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

Keywords. Contact manifold, symplectic filling, symplectic Lefschetz fibration, open book decomposition

AMS subject classification. Primary: 53C15. Secondary: 57M50.

DOI: 10.2140/gt.2004.8.277

E-print: arXiv:math.SG/0311459

Submitted to GT on 25 November 2003. (Revised 13 January 2004.) Paper accepted 2 January 2004. Paper published 14 February 2004.

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Yakov Eliashberg
Department of Mathematics, Stanford University
Stanford CA 94305-2125, USA
Email: eliash@gauss.stanford.edu

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