Contact manifolds and Weinstein $h$-cobordisms

We prove that closed connected contact manifolds of dimension $2n - 1 \geqslant 5$ related by a flexible Weinstein $h$-cobordism become contactomorphic after contact connect-summing with $S^k \times S^{2n-k-1}$ with $2 \leqslant k \leqslant n - 1$. We also provide examples of non-conjugate contact structures on a closed manifold with exact symplectomorphic symplectizations.

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Published 12 September 2016