University of Georgia
Mathematics Department Colloquium
Professor Vincente Colin
University of Nantes
January 16, 2003
On the coarse classification of contact structures in dimension 3
In dimension 3, contact structures and
foliations are the only plane fields which are locally
homogeneous. This means that their study should reflect the geometry
of the ambient manifold. We'll give a classification result for the
most interesting class of contact structures: the tight ones. A
closed, orientable, irreducible 3-manifold carries infinitely many
tight contact structures if and only if it contains a pi_1-injected
2-torus. This is a joint work with Emmanuel Giroux and Ko
Honda.