Published Paper

Inserted: 12 jul 2022
Last Updated: 12 mar 2023

Journal: Journal of the London Mathematical Society
Volume: 107(3)
Pages: 943--97
Year: 2023

Abstract:

We show two stability results for a closed Riemannian manifold whose Ricci curvature is small in the Kato sense and whose first Betti number is equal to the dimension. The first one is a geometric stability result stating that such a manifold is Gromov-Hausdorff close to a flat torus. The second one states that, under a stronger assumption, such a manifold is diffeomorphic to a torus: this extends a result by Colding and Cheeger-Colding obtained in the context of a lower bound on the Ricci curvature.

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• CMT_Betti.pdf