New Topological Restrictions For Spaces With Nonnegative Ricci Curvature
Differential Geometry
2026-01-21 v1 Geometric Topology
Metric Geometry
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.
Cite
@article{arxiv.2601.14231,
title = {New Topological Restrictions For Spaces With Nonnegative Ricci Curvature},
author = {Alessandro Cucinotta and Mattia Magnabosco and Daniele Semola},
journal= {arXiv preprint arXiv:2601.14231},
year = {2026}
}