Weak and strong fillability of higher dimensional contact manifolds

By Patrick Massot, Klaus Niederkruger, Chris Wendl. 2011

113 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f2e8e32e04f14cd57984595796d81bf4d8c54b88

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Geometric criteria for overtwistedness (2015, unknown): “Proposition 8.2 also holds in higher dimensions for any weakly ﬁllable contact structure ( Y 2 n − 1 , ker α ), as follows by combining F. Bourgeois’ construction [5] of contact structures in Y × T 2 and the observation [42, Example 1.1] that the construction preserves weak ﬁllability.”
Symplectic homology and the Eilenberg-Steenrod axioms (2015, background): “Other examples are the 3-torus T 3 with a Giroux contact structure ξk = ker ( cos(ks)dθ+sin(ks)dt ) and its higherdimensional generalizations (T (2)×N, ξk) by Massot–Niederkrüger–Wendl [58].”