Weak and strong fillability of higher dimensional contact manifolds
نویسندگان
چکیده
منابع مشابه
On fillability of contact manifolds
The aim of this text is to give an accessible overview to some recent results concerning contact manifolds and their symplectic fillings. In particular, we work out the weakest compatibility conditions between a symplectic manifold and a contact structure on its boundary to still be able to obtain a sensible theory (Chapter II), furthermore we prove two results (Theorem A and B in Section I.4) ...
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According to Lerman, compact connected toric contact 3-manifolds with a non-free toric action whose moment cone spans an angle greater than π are overtwisted, thus non-fillable. In contrast, we show that all compact connected toric contact manifolds in dimension greater than three are weakly symplectically fillable and most of them are strongly symplectically fillable. The proof is based on the...
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Recently, P. Ozsváth and Z. Szabó defined an invariant of contact structures with values in the Heegaard-Floer homology groups. They also proved that the twisted invariant of a weakly symplectically fillable contact structures is non trivial. In this article we prove with an example that their non vanishing result does not hold in general for the untwisted contact invariant. As a consequence of...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2012
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-012-0412-5