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

References in corpus (4)

• Minimality and irreducibility of symplectic four-manifolds
• A simply connected surface of general type with p_g=0 and K^2=4
• The Normalized Ricci Flow on Four-Manifolds and Exotic Smooth Structures
• Smooth Structures and Normalized Ricci Flows on Non-Simply Connected Four-Manifolds

Cited by in corpus (1)

• Smooth Structures and Normalized Ricci Flows on Non-Simply Connected Four-Manifolds