  In this article we show that every closed oriented smooth 4-manifold can be
decomposed into two codimension zero submanifolds (one with reversed
orientation) so that both pieces are exact Kahler manifolds with strictly
pseudoconvex boundaries and that induced contact structures on the common
boundary are isotopic. Meanwhile, matching pairs of Lefschetz fibrations with
bounded fibers are offered as the geometric counterpart of these structures. We
also provide a simple topological proof of the existence of folded symplectic
forms on 4-manifolds.
