Four-dimensional symplectic cobordisms containing three-handles

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dc.creatorGay, David T
dc.date2006-06-16
dc.date2009-03-02
dc.date.accessioned2026-07-07T12:47:45Z
dc.date.available2026-07-07T12:47:45Z
dc.descriptionWe 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.
dc.descriptionThis is the version published by Geometry & Topology on 28 October 2006
dc.identifierhttps://arxiv.org/abs/math/0606402
dc.identifierhttp://arxiv.org/abs/math/0606402
dc.identifierGeom. Topol. 10 (2006) 1749-1759
dc.identifierdoi:10.2140/gt.2006.10.1749
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221826
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.subject53D35, 57R17, 53D20, 57M50
dc.titleFour-dimensional symplectic cobordisms containing three-handles
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