Universal covers of non-negatively curved manifolds and formality
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909232867049472 |
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| author | Milivojevic, Aleksandar |
| author_facet | Milivojevic, Aleksandar |
| contents | We show that if the universal cover of a closed smooth manifold admitting a metric with non-negative Ricci curvature is formal, then the manifold itself is formal. We reprove a result of Fiorenza-Kawai-Lê-Schwachhöfer, that closed orientable manifolds with a non-negative Ricci curvature metric and sufficiently large first Betti number are formal. Our method allows us to remove the orientability hypothesis; we further address some cases of non-closed manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal covers of non-negatively curved manifolds and formality Milivojevic, Aleksandar Differential Geometry Algebraic Topology 55P62, 57R19, 53C25 We show that if the universal cover of a closed smooth manifold admitting a metric with non-negative Ricci curvature is formal, then the manifold itself is formal. We reprove a result of Fiorenza-Kawai-Lê-Schwachhöfer, that closed orientable manifolds with a non-negative Ricci curvature metric and sufficiently large first Betti number are formal. Our method allows us to remove the orientability hypothesis; we further address some cases of non-closed manifolds. |
| title | Universal covers of non-negatively curved manifolds and formality |
| topic | Differential Geometry Algebraic Topology 55P62, 57R19, 53C25 |
| url | https://arxiv.org/abs/2406.19539 |