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.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3050