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.
On the $σ_2$-curvature and volume of compact manifolds
A local version of Bando's theorem on the real-analyticity of solutions to the Ricci flow
Decompositions of the space of Riemannian metrics on a compact manifold with boundary
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