5-dimensional Bourgeois contact structures are tight

Abstract

Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction for a contact structure on $V\times {\mathbb{T}}^2$. We prove that all such structures are universally tight in dimension $5$, independent on whether the original contact manifold is tight or overtwisted.

This manuscript is withdrawn, since it has been superseded (and is strictly contained in) the article in arXiv:1908.05749