On the construction of contact submanifolds with prescribed topology

We prove the existence of contact submanifolds realizing the Poincare dual of the top Chern class of a complex vector bundle over a closed contact man ifold. This result is analogue in the contact category to Donaldson's const ruction of symplectic submanifolds. The main tool in the construction is to show the existence of sequences of sections which are asymptotically holom orphic in an appropiate sense and that satisfy a transversality with estima tes property directly in the contact category. The description of the obtai ned contact submanifolds allows us to prove an extension of the Lefschetz h yperplane theorem which completes their topological characterization.