___________________________________________________________________________ MARTEDI` 20 NOVEMBRE 2007

SEMINARI DI GEOMETRIA 15:00-16:00, Sala Seminari (Dip. Matematica "L. Tonelli") Geodesible contact structures Patrick Massot (ENS, Lyon)

Abstract: A plane field P is geodesible if there is some Riemannian metric g such that every geodesic of g which is somewhere tangent to P is everywhere tangent to P. The work of Carrière in the 80's gives a very simple characterization of geodesible plane fields on 3-manifolds. In this talk we will explain how topological techniques allow to understand geodesible contact structures in dimension 3, especially on Seifert manifolds. This study involves many connections between contact topology, symplectic and complex geometry and foliation theory (basic definitions will be recalled).

SEMINARI DI GEOMETRIA 16:15-17:15, Sala Seminari (Dip. Matematica "L. Tonelli") Contact manifolds as boundaries of symplectic manifolds Klaus Niederkrüger (ENS, Lyon)

Abstract: The "typical" example of a contact manifold was thought to be the convex boundary of a symplectic manifold. Eliashberg and Gromov discovered a criterion called "overtwistedness" which shows that some contact 3-manifolds are not a convex boundary of any manifold. In fact, it followed that almost all contact 3-manifolds are overtwisted.

I will try to explain these notions, and give a sketch of the proof of Eliashberg and Gromov. If time permits, I will briefly explain generalizations to higher dimensional contact manifolds. ___________________________________________________________________________

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