On Normalized Ricci Flow and Smooth Structures on Four-Manifolds with $b^+=1$

Ishida, Masashi; Rasdeaconu, Rares; Suvaina, Ioana

On Normalized Ricci Flow and Smooth Structures on Four-Manifolds with $b^+=1$

Authors

Ishida, Masashi

Rasdeaconu, Rares

Suvaina, Ioana

Description

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 ${\mathbb C}{P}^2 # l \overline{{\mathbb C}{P}^2}$, where $5 \leq l \leq 8$.