Sylvain Courte

PhD Thesis

I did my PhD Thesis, entitled H-cobordisms in symplectic geometry, at ENS Lyon under the supervision of Emmanuel Giroux. The defense took place on June, 4th 2015. Here are the manuscript and the slides used for the defense.

Research articles

Contact manifolds with symplectomorphic symplectizations

Geometry & Topology 18 (2014) 1–15.

In this article, we construct, in every odd dimension greater than or equal to 5, examples of non diffeomorphic closed contact manifolds having symplectomorphic symplectizations.

published version, arXiv version


Contact manifolds and Weinstein h-cobordisms

Journal of Symplectic Geometry 14 (3) 2016 657-669.

This article contains two main results. The first one is a stabilization theorem : the contact manifolds constructed in the article above become contactomorphic after sufficiently many connected sum with a product of spheres. The second one is an example, in every odd dimension greater than or equal to five, of a closed manifold carrying non conjugate contact structures with symplectomorphic symplectizations.

published version, arXiv version


Legendrian submanifolds with hamiltonian isotopic symplectizations

Algebraic & Geometric Topology 16 (2016) 3641–3652.

In any contact manifold of dimension greater than or equal to 11, we construct closed Legendrian submanifolds which are not diffeomorphic but whose lagrangian cylinders in the symplectization are hamiltonian isotopic. We make essential use of the notion of flexible lagrangian cobordism recently introduced by Eliashberg, Ganatra et Lazarev.

published version, arXiv version