Weak and strong fillability of higher dimensional contact manifolds

Details Weak and strong fillability of higher dimensional contact manifolds Weak and strong fillability of higher dimensional contact manifolds

2011-11-25

arxiv.org/abs/1111.6008v2

Mathematics

Symplectic Geometry

68 pages, 5 figures. v2: Some attributions clarified, and other minor edits

Scientific paper

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.

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