Decomposing four-manifolds up to homotopy type

Let M be a closed connected oriented topological 4-manifold. Suppose that there is a degree one map f from M to another closed topological 4-manifold P, which induces an isomorphism between the fundamental groups. We give a homological condition on the integer intersection form of M and on the intersection form of M over the integral group ring of its fundamental group under which M is homotopy equivalent to a connected sum of P with a simply-connected closed topological 4-manifold M'. This gives a partial solution to a conjecture of Hillman stated in Bull. London Math. Soc. 27 (1995). Then some splitting results for closed 4-manifolds with special homotopy complete the paper