On properties of Bourgeois contact structures

Abstract

The Bourgeois construction associates to every contact open book on a manifold $V$ a contact structure on $V\times {\mathbb{T}}^2$. We study some of the properties of $V$ that are inherited by $V\times {\mathbb{T}}^2$ and some that are not.

Giroux has provided recently a better framework to work with contact open books. In the appendix, we quickly review this formalism, and we work out a few classical examples of contact open books to illustrate how to use this new language.