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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.21078 |
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| _version_ | 1866911686398574592 |
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| author | Chen, Zhengnan |
| author_facet | Chen, Zhengnan |
| contents | In [Bre19], Simon Brendle showed that any compact manifold of dimension $n\geq12$ with positive isotropic curvature and contains no nontrivial incompressible $(n-1)-$dimensional space form is diffeomorphic to a connected sum of finitely many spaces, each of which is a quotient of $S^n$ or $S^{n-1}\times \mathbb{R}$ by standard isometries. We show that this result is actually true for $n\geq9$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Manifolds with positive isotropic curvature of dimension at least nine Chen, Zhengnan Differential Geometry In [Bre19], Simon Brendle showed that any compact manifold of dimension $n\geq12$ with positive isotropic curvature and contains no nontrivial incompressible $(n-1)-$dimensional space form is diffeomorphic to a connected sum of finitely many spaces, each of which is a quotient of $S^n$ or $S^{n-1}\times \mathbb{R}$ by standard isometries. We show that this result is actually true for $n\geq9$. |
| title | Manifolds with positive isotropic curvature of dimension at least nine |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.21078 |