Stable classification of 4-manifolds with 3-manifold fundamental groups, I

Abstract:
In the first part, we review the stable classification program of 4-manifolds using Kreck's modified surgery. In the second part, we will consider smooth spin 4-manifolds whose fundamental group is that of an aspherical, oriented 3-manifold. In this case, we will give a complete set of invariants that determine whether two such manifolds are stably diffeomorphic.