On Symplectic Fillings
Algebr. Geom. Topol. 4 (2004), 73-80.

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic manifold. We also relate properties of the open book decomposition of a contact manifold its possible fillings. These results are also useful in showing the contact Heegaard Floer invariant of a fillable contact structure do not vanish, see [27], and property P for knots, see [17].

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