A splitting theorem for homotopy equivalent 4-manifolds

We prove a decomposition theorem for closed connected homotopy equivalent smooth four-manifolds, which partially extends a recent result of Curtis, Freedman, Hsiang and Stong, Invent. Math., 123 (1996), to the non-simply connected case. Then we study the question of when a homotopy equivalence between closed smooth 4-manifolds is homotopic to a topological homeomorphism. In particular, we obtain a new proof of the well-known uniqueness of closed aspherical smooth 4-manifolds with good fundamental groups.