Definite four-manifolds with exotic smooth structures

In this paper, we study smooth structures on closed, oriented four-manifolds with fundamental group Z/2Z and definite intersection form. We construct infinitely many irreducible, oriented, closed, definite, smooth four-manifolds with π1 = Z/2Z and b2 = 1, and b2 = 2. As an application, we prove that, when the second Betti number b2 of a definite four-manifold with π1 = Z/2Z is positive and it admits a smooth structure, then it admits infinitely many smooth structures.