Non-exact symplectic cobordisms between contact 3-manifolds

Chris Wendl University College London

Differential Geometry mathscidoc:1609.10328

Journal of Differential Geometry, 95, (1), 121-182, 2013
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 Σ × D and Σ × [−1, 1] × S1, which have symplectic cores and can be attached to contact 3-manifolds along sufficiently large neighborhoods of transverse links and preLagrangian 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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  author={Chris Wendl},
  booktitle={Journal of Differential Geometry},
Chris Wendl. NON-EXACT SYMPLECTIC COBORDISMS BETWEEN CONTACT 3-MANIFOLDS. 2013. Vol. 95. In Journal of Differential Geometry. pp.121-182.
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