Constructions of contact manifolds

Abstract

1. Introduction

It has been known for some time that contact structures show a high degree of topological flexibility in the sense that many topological operations can be performed on contact manifolds while preserving the contact property. For instance, Martinet [14] used a surgery description of 3-manifolds to show that every closed, oriented 3-manifold admits a contact structure, and alternative proofs of this result were given later by Thurston and Winkelnkemper [18], who based their proof on an open book decomposition, and Gonzalo [8], who used branched covers. These, however, are all strictly 3-dimensional constructions.