Two 4-manifolds are said to be $\mathbb CP^2$-stably diffeomorphic if after connected sum with arbitrarily many copies of the complex projective plane, they become diffeomorphic. We show that for many fundamental groups the classification of 4-manifolds up to $\mathbb CP^2$-stable diffeomorphism is determined by the homotopy 2-type.

This is joint work with Mark Powell and Peter Teichner.