New Topological Restrictions For Spaces With Nonnegative Ricci Curvature
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909996044779520 |
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| author | Cucinotta, Alessandro Magnabosco, Mattia Semola, Daniele |
| author_facet | Cucinotta, Alessandro Magnabosco, Mattia Semola, Daniele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14231 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New Topological Restrictions For Spaces With Nonnegative Ricci Curvature Cucinotta, Alessandro Magnabosco, Mattia Semola, Daniele Differential Geometry Geometric Topology Metric Geometry 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. |
| title | New Topological Restrictions For Spaces With Nonnegative Ricci Curvature |
| topic | Differential Geometry Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2601.14231 |