A Theorem of Eliashberg and Thurston on Foliations and Contact Structures

These notes originate from a seminar held in Pisa in November and December 1996 jointly by Riccardo Benedetti, Paolo Lisca and me. The aim of these notes is to give a detailed proof of the following result due to Eliashberg and Thurston: THM Let M be a closed oriented 3-manifold and let F be a cooriented C2-smooth codimension-1 foliation on M. Assume that (M,F) is not diffeomorphic to the product foliation on S2xS1. Then arbitrarily close to F in the C0 topology there exist a positive and a negative C\infty contact structure.