21/06/2001, 13:00 — 14:00 — Amphitheatre Ea2, North Tower, IST
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.