 A result of Joseph J. Kohn states that global embeddability is equivalent to the condition that the Kohn Laplacian have closed range.This condition of closed range is not a CR invariant condition.In dimension 3, a non-perturbative set of conditions that are CR invariant has been found by Sagun Chanillo, Hung-Lin Chiu and Paul C. Yang that guarantees global embeddability for abstract strongly pseudo-convex CR structures defined on compact manifolds.