Classification of compact manifolds with positive isotropic curvature
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912713567895552 |
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| author | Huang, Hong |
| author_facet | Huang, Hong |
| contents | We show the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a quotient manifold of $\mathbb{S}^{n-1}\times \mathbb{R}$ by a cocompact discrete subgroup of the isometry group of the round cylinder $\mathbb{S}^{n-1}\times \mathbb{R}$, or a connected sum of a finite number of such manifolds. This extends previous works of Brendle and Chen-Tang-Zhu, and improves a work of Huang. The proof uses Ricci flow with surgery on compact orbifolds, with the help of the ambient isotopy uniqueness of closed tubular neighborhoods of compact embedded full suborbifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18154 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of compact manifolds with positive isotropic curvature Huang, Hong Differential Geometry We show the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a quotient manifold of $\mathbb{S}^{n-1}\times \mathbb{R}$ by a cocompact discrete subgroup of the isometry group of the round cylinder $\mathbb{S}^{n-1}\times \mathbb{R}$, or a connected sum of a finite number of such manifolds. This extends previous works of Brendle and Chen-Tang-Zhu, and improves a work of Huang. The proof uses Ricci flow with surgery on compact orbifolds, with the help of the ambient isotopy uniqueness of closed tubular neighborhoods of compact embedded full suborbifolds. |
| title | Classification of compact manifolds with positive isotropic curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2305.18154 |