Can a Good Manifold Come to a Bad End?

Two notions of cobordism are defined for compact CR-manifolds. The weaker notion, complex cobordism realizes two CR-manifolds as the boundary of a complex manifold; in the stronger notion, strict complex cobordism there is a strictly plurisubharmonic function defined on the total space of the cobordism with the boundary components as level sets of this function. We show that embeddability for a 3-dimensional, strictly pseudoconvex CR-manifold is a strict cobordism invariant. De Oliveira has recently shown that this is false for complex cobordisms. His construction is described in an appendix. Date: October 11, 2000, corrected April 17, 2006 ; Run: April 17, 2006