Nonsmoothable group actions on spin $4$–manifolds

Abstract

We show that every closed, simply connected, spin topological $4$–manifold except $S^4$ and $S^2\times S^2$ admits a homologically trivial, pseudofree, locally linear action of ${\mathbb{Z}}_p$ for any sufficiently large prime number $p$ which is nonsmoothable for any possible smooth structure.