Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$

Wen Shen

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arXiv · 2510.00613

Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$

Wen Shen

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Abstract

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 $\Sigma^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-actions on $S^7\times S^7$.

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Wen Shen. 2025-10-01. Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$. https://arxiv.org/abs/2510.00613

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