Preimages of CR submanifolds with generic holomorphic maps

We investigate the notion of CR transversality of a generic holomorphic map f: ℂ ⁿ → ℂ ^m to a smooth CR submanifold M of ℂ ^m . We construct a stratification of the set of non-CR transversal points in the preimage M′ = f ⁻¹ (M) by smooth submanifolds, consisting of points where the CR dimension of M′ is constant. We show the existence of a Whitney stratification for sets which are locally diffeomorphic to the product of an open set and an analytic set. Work on this paper was supported by ARRS, Republic of Slovenia.