# 5-dimensional Bourgeois contact structures are tight

## TL;DR

This paper proves that all 5-dimensional Bourgeois contact structures, constructed from a supporting open book decomposition, are universally tight regardless of the tightness or overtwistedness of the original contact manifold.

## Contribution

It establishes the universal tightness of all 5-dimensional Bourgeois contact structures, a result previously unknown in contact topology.

## Key findings

- All such structures are universally tight in dimension 5.
- The tightness holds regardless of the original manifold's tightness.
- The result applies to both tight and overtwisted initial contact manifolds.

## 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.

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Source: https://tomesphere.com/paper/1903.11866