The Nielsen realization for non-spin 4-manifolds

We are going to show that there are many families of non-spin 4–manifolds for which the smooth Nielsen realization problem fails; that is, there are (finite) subgroups of their mapping class groups that cannot be realized by a group of diffeomorphisms. This extends and complements the recent results for spin 4–manifolds. This is joint work with Inanc Baykur.