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2006 Four-dimensional symplectic cobordisms containing three-handles
David T Gay
Geom. Topol. 10(3): 1749-1759 (2006). DOI: 10.2140/gt.2006.10.1749


We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other key feature is that these cobordisms contain chains of symplectically embedded two-spheres of square zero. This, together with standard gauge theory, is used to show that any contact three-manifold of non-zero torsion (in the sense of Giroux) cannot be strongly symplectically fillable. John Etnyre pointed out to the author that the same argument together with compactness results for pseudo-holomorphic curves implies that any contact three-manifold of non-zero torsion satisfies the Weinstein conjecture. We also get examples of weakly symplectically fillable contact three-manifolds which are (strongly) symplectically cobordant to overtwisted contact three-manifolds, shedding new light on the structure of the set of contact three-manifolds equipped with the strong symplectic cobordism partial order.


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David T Gay. "Four-dimensional symplectic cobordisms containing three-handles." Geom. Topol. 10 (3) 1749 - 1759, 2006.


Received: 22 June 2006; Accepted: 13 October 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1129.53061
MathSciNet: MR2284049
Digital Object Identifier: 10.2140/gt.2006.10.1749

Primary: 53D35, 57R17
Secondary: 53D20, 57M50

Rights: Copyright © 2006 Mathematical Sciences Publishers


Vol.10 • No. 3 • 2006
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