Open Access
September 2013 Non-exact symplectic cobordisms between contact 3-manifolds
Chris Wendl
J. Differential Geom. 95(1): 121-182 (September 2013). DOI: 10.4310/jdg/1375124611


We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of contact 3-manifolds which are symplectically cobordant to something overtwisted, or to the tight 3-sphere, or which admit symplectic caps containing symplectically embedded spheres with vanishing self-intersection. These constructions imply new and simplified proofs of several recent results involving fillability, planarity, and non-separating contact type embeddings. The cobordisms are built from symplectic handles of the form $\Sigma \times \mathbb{D}$ and $\Sigma \times [−1, 1] \times S^1$, which have symplectic cores and can be attached to contact 3-manifolds along sufficiently large neighborhoods of transverse links and pre- Lagrangian tori. We also sketch a construction of $J$-holomorphic foliations in these cobordisms and formulate a conjecture regarding maps induced on Embedded Contact Homology with twisted coefficients.


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Chris Wendl. "Non-exact symplectic cobordisms between contact 3-manifolds." J. Differential Geom. 95 (1) 121 - 182, September 2013.


Published: September 2013
First available in Project Euclid: 29 July 2013

zbMATH: 1278.57037
MathSciNet: MR3128981
Digital Object Identifier: 10.4310/jdg/1375124611

Rights: Copyright © 2013 Lehigh University

Vol.95 • No. 1 • September 2013
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