Cursos de Verão em Geometria 

21/06/2001, 13:00 — 14:00 — Anfiteatro Ea2, Torre Norte (Electricidade)
Charles Epstein, University of Pennsylvania

Survey of the geometric and analytic results in contact structures (II)

Filling three dimensional CR-manifolds. Three dimensional CR-manifolds have, in some sense, too many deformations because most cannot be realized as the boundaries of Stein spaces. This problem is related to that of finding symplectic fillings for contact manifolds. We give examples and consider the general features of this pathology. Lempert's algebraic approximation theorem gives a way to address this problem. We introduce this approach and consider the case of hypersurfaces in lines bundles over \(P^1\) in detail. We define the relative index which provides a measure of the change in the algebra of CR-functions under a deformation of the CR-structure.