On properties of Bourgeois contact structures

Abstract

The Bourgeois construction associates to every contact open book on a manifold $V$ a contact structure on $V\times T^2$. We study in this article some of the properties of $V$ that are inherited by $V\times T^2$ and some that are not. Giroux has provided recently a suitable framework to work with contact open books. In the appendix of this article, 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.

25 pages; reorganized structure of paper, addressed Gironella's work on Bourgeois structures, improved exposition and added examples

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Contact homology and virtual fundamental cycles
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Examples of non-trivial contact mapping classes in all dimensions
• On some examples and constructions of contact manifolds

Cited by in corpus (2)

• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• On some examples and constructions of contact manifolds