On the topology and geometry of certain $13$-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929719742562304 |
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| author | Shen, Wen |
| author_facet | Shen, Wen |
| contents | This paper gives the classifications of certain manifolds $\mathcal{M}$ of dimension $13$ up to diffeomorphism, homeomorphism, and homotopy equivalence, whose cohomology rings are isomorphic to $H^\ast(\mathrm{CP}^3\times S^7;\mathbb{Z})$. Moreover, we prove that either $\mathcal{M}$ or $\mathcal{M}\#Σ^{13}$ admits a metric of non-negative sectional curvature where $Σ^{13}$ is a certain exotic sphere of dimension 13. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the topology and geometry of certain $13$-manifolds Shen, Wen Geometric Topology Algebraic Topology 57R19, 57R50, 53C20 This paper gives the classifications of certain manifolds $\mathcal{M}$ of dimension $13$ up to diffeomorphism, homeomorphism, and homotopy equivalence, whose cohomology rings are isomorphic to $H^\ast(\mathrm{CP}^3\times S^7;\mathbb{Z})$. Moreover, we prove that either $\mathcal{M}$ or $\mathcal{M}\#Σ^{13}$ admits a metric of non-negative sectional curvature where $Σ^{13}$ is a certain exotic sphere of dimension 13. |
| title | On the topology and geometry of certain $13$-manifolds |
| topic | Geometric Topology Algebraic Topology 57R19, 57R50, 53C20 |
| url | https://arxiv.org/abs/2406.15697 |