abstract: It is a fascinating problem in four-dimensional topology to determine which topological four-manifolds admit more than one (or even infinitely many) distinct smooth structures. This question is wide open for some basic examples like the four-sphere, the four-torus and the complex projective plane. In collaboration with Inanc Baykur and Zoltán Szabó we have made some progress in the case when the fundamental group of the closed four-manifold is a cyclic group of even order.