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arXiv · 2601.14231

New Topological Restrictions For Spaces With Nonnegative Ricci Curvature

Alessandro Cucinotta·Mattia Magnabosco·Daniele Semola
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Abstract

We obtain new topological restrictions for complete Riemannian manifolds with nonnegative Ricci curvature and RCD(0,n) spaces. Our main results are a Betti number rigidity theorem which answers a question open since work of M.-T. Anderson in 1990, and a vanishing theorem for the simplicial volume generalizing a theorem of M. Gromov from 1982. Combining such results we obtain a new proof of the classification of noncompact 3-manifolds with nonnegative Ricci curvature, originally due to G. Liu in 2011, which extends to the synthetic setting.

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Alessandro Cucinotta, Mattia Magnabosco, Daniele Semola. 2026-01-20. New Topological Restrictions For Spaces With Nonnegative Ricci Curvature. https://arxiv.org/abs/2601.14231

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