Positive scalar curvature metrics and aspherical summands
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918252997771264 |
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| author | Chen, Shuli Chu, Jianchun Zhu, Jintian |
| author_facet | Chen, Shuli Chu, Jianchun Zhu, Jintian |
| contents | We prove for $n\in\{3,4,5\}$ that the connected sum of a closed aspherical $n$-manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative scalar curvature. In particular, a special case of our result answers a question of Gromov.
More generally, we generalize the partial classification result of Chodosh, Li, and Liokumovich to the non-compact domination case with our newly-developed technique.
Our result unifies all previous results of this type, and confirms the validity of Gromov's non-compact domination conjecture for closed aspherical manifolds of dimensions 3, 4, and 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04698 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positive scalar curvature metrics and aspherical summands Chen, Shuli Chu, Jianchun Zhu, Jintian Differential Geometry Geometric Topology 53C21, 53A10 We prove for $n\in\{3,4,5\}$ that the connected sum of a closed aspherical $n$-manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative scalar curvature. In particular, a special case of our result answers a question of Gromov. More generally, we generalize the partial classification result of Chodosh, Li, and Liokumovich to the non-compact domination case with our newly-developed technique. Our result unifies all previous results of this type, and confirms the validity of Gromov's non-compact domination conjecture for closed aspherical manifolds of dimensions 3, 4, and 5. |
| title | Positive scalar curvature metrics and aspherical summands |
| topic | Differential Geometry Geometric Topology 53C21, 53A10 |
| url | https://arxiv.org/abs/2312.04698 |