Geometry & Topology, Vol. 8 (2004)
Paper no. 6, pages 277--293.
A few remarks about symplectic filling
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.
Contact manifold, symplectic filling, symplectic Lefschetz fibration,
open book decomposition
AMS subject classification.
Submitted to GT on 25 November 2003.
(Revised 13 January 2004.)
Paper accepted 2 January 2004.
Paper published 14 February 2004.
Notes on file formats
Department of Mathematics, Stanford University
Stanford CA 94305-2125, USA
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