G\'eom\'etrie de contact: de la dimension trois vers les dimensions sup\'erieures

TL;DR

This paper explores the connections between the global geometry of closed contact manifolds and the geometry of Stein compact symplectic manifolds they bound, emphasizing the role of open book decompositions in establishing these relations.

Contribution

It establishes a link between contact geometry and symplectic Stein manifolds through the use of open book decompositions adapted to contact structures.

Findings

Relations between contact and symplectic geometries are described.

Open book decompositions are key to understanding these relations.

The work advances understanding of contact structures in higher dimensions.

Abstract

On d\'ecrit ici des relations entre la g\'eom\'etrie globale des vari\'et\'es de contact closes et celle de certaines vari\'et\'es symplectiques, \`a savoir les vari\'et\'es de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adapt\'es aux structures de contact. We discuss relations between the global geometry of closed contact manifolds and the geometry of compact symplectic Stein manifolds that they bound. The origin of these relations is the existence of open book decompositions adapted to contact structures.