Stable Classification of 4-manifolds

In the first part of the talk, as a warm-up, I will remind the audience of Freedmans classification
of simply connected 4-manifolds. I will then go over to the weaker classification up to stable homeomorphism
and explain how this is related to calculating bordism groups and explain the role the fundamental group plays.
In the second part I will then report on a joint paper with D. Kasprowski, M. Powell and P. Teichner about the
stable classification of 4-manifolds whose fundamental group is COAT, i.e. that of a closed orientable aspherical three-manifold.