On normalized Ricci flow and smooth structures on four-manifolds with b + = 1

Abstract

We find an obstruction to the existence of non-singular solutions to the normalized Ricci flow on four-manifolds with b+ = 1. By using this obstruction, we study the relationship between the existence or non-existence of non-singular solutions of the normalized Ricci flow and exotic smooth structures on the topological 4-manifolds \(\mathbb{C}P^{2} {\# \ell}{\overline{{\mathbb{C}}P^2}}\), where \(5 \leq \ell \leq 8\).