Contact manifolds and Weinstein h-cobordisms
  We prove that closed connected contact manifolds of dimension $\geq 5$ related by an h-cobordism with a flexible Weinstein structure become contactomorphic after some kind of stabilization. We also provide examples of non-conjugate contact structures on a closed manifold with exact symplectomorphic symplectizations. 
Sylvain Courte
math.SG