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

Daniel Kasprowsky (Max Planck Institute)

By Kreck's modified surgery the question whether two closed, smooth, spin 4-manifolds M,M' with fundamental group G are stably diffeomorphic can be approached by computing the spin-bordism group of the classifying space BG. We study the situation where the fundamental group of M is that of an closed, oriented, aspherical 3-manifold and show that in this case M,M' are stably diffeomorphic if and only if they have the same fundamental group and their equivariant intersection forms are stably isomorphic.