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Uniqueness of the contact structure approximating a foliation

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Thomas Vogel
Don, 11/04/2013 - 16:30 - 17:30
MPIM Lecture Hall

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.

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