A lower bound for the diameter of solutions to the Ricci flow with nonzero $H^{1}(M^{n};R)$

Abstract

We obtain a lower bound for the diameter of a solution to the Ricci flow on a compact manifold with nonvanishing first real cohomology. A consequence of our result is an affirmative answer to Hamilton's conjecture that a product metric on $(S^{1}\times S^{n-1}$ cannot arise as a final time limit flow.