Self-homeomorphisms of 4-manifolds with fundamental group Z

In this paper we study the classification of self-homeomorphisms of closed, connected, oriented 4-manifolds with infinite cyclic fundamental group up to pseudoisotopy, or equivalently up to homotopy. We find that for manifolds with even intersection form homeomorphisms are classified up to pseudoisotopy by their action on π1 , π2 and the set of spin structures on the manifold. For manifolds with odd intersection form they are classified by the action on π1 and π2 and an additional Z/2Z . As a consequence we complete the classification program for closed, connected, oriented 4-manifolds with infinite cyclic fundamental group, begun by Freedman, Quinn and Wang.