Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914069930311680 |
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| author | Shen, Wen |
| author_facet | Shen, Wen |
| contents | In this paper, we classify simply connected closed smooth $13$-dimensional manifolds whose cohomology ring is isomorphic to that of $\mb{CP}^3\times S^7$, up to diffeomorphism, homeomorphism, and homotopy equivalence. Furthermore, if such a manifold satisfies certain conditions, either itself or its connected sum with an exotic $13$-sphere $Σ^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-actions on $S^7\times S^7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$ Shen, Wen Algebraic Topology Geometric Topology In this paper, we classify simply connected closed smooth $13$-dimensional manifolds whose cohomology ring is isomorphic to that of $\mb{CP}^3\times S^7$, up to diffeomorphism, homeomorphism, and homotopy equivalence. Furthermore, if such a manifold satisfies certain conditions, either itself or its connected sum with an exotic $13$-sphere $Σ^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-actions on $S^7\times S^7$. |
| title | Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$ |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2510.00613 |