Uniqueness of the contact structure approximating a foliation

According to a theorem of Eliashberg and Thurston a C²-foliation on a closed 3-manifold can be C⁰-approximated by contact structures unless all leaves of the foliation are spheres. Examples on the 3-torus show that every neighbourhood of  a foliation can contain
infinitely many non-diffeomorphic contact structures. In this talk we show that this is rather exceptional: In many interesting situations the contact structure in a sufficiently small
neighbourhood of the foliation is uniquely determined up to isotopy. This fact can be
applied to obtain results about the topology of the space of taut foliations.