The normalized Ricci flow on four-manifolds and exotic smooth structures

We shall prove that, for every natural number $\ell$ there exists a closed topological $4$-manifold $X_{\ell}$ which admits smooth structures for which non-singular solutions of the normalized Ricci flow exist, but also admits smooth structures for which no non-singular solution of the normalized Ricci flow exists. Hence, in dimension $4$, smooth structures become definite obstructions to the existence of non-singular solutions to the normalized Ricci flow.

Keywords

Ricci flow, non-singular solution, exotic smooth structure

2010 Mathematics Subject Classification

53C21, 53C44, 57R57

Full Text (PDF format)

Published 22 February 2017