Nonsmoothable actions of \(\mathbb{Z}_2\times\mathbb{Z}_2\) on spin four-manifolds (Q2072120)

There are many differences between the categories of smooth and topological \(4\) manifolds. This also applies to group actions on \(4\) manifolds. The author constructs families of locally linear actions of \(\mathbb Z_2 \times \mathbb Z_2\) so that the action of each proper subgroup is smooth for some smooth structure on the manifold, but the action of the whole group is not smooth for any smooth structure on it. There are results of others along the same lines, and the author reviews them.