Invariant Kohn-Rossi cohomology and obstruction to embedding of compact real (2n-1)-dimensional CR manifolds in C~N

摘要

Let X be a compact connected CR manifold of real dimension 2n - 1. One of the most important invariants in C R-geometry is the Kohn-Rossi cohomology H_(K R)~(p,q)(X) introduced by Kohn and Rossi in 1965 [Ko-Ro]. Throughout this paper , we shall assume that n ≧3 and X is strongly pseudoconvex. As a consequence of Kohn's solution to the partial deriv -Neumann problem, Kohn-Rossi showed that H_(K R)~(p,q)(X) is finite dimensional if 1 ≦ q ≦ n-2. In 1974, Boutet de Monvel [Bo] (see also Kohn [Ko_3]) proved that X is C R -embeddable in some C~N. There are two fundamental questions raised by the theorem of Boutet de Monvel.