On the topology and geometry of certain $13$-manifolds

Wen Shen

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arXiv · 2406.15697

On the topology and geometry of certain $13$-manifolds

Wen Shen

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Abstract

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 $\mathcal{M}\#\Sigma^{13}$ admits a metric of non-negative sectional curvature where $\Sigma^{13}$ is a certain exotic sphere of dimension 13.

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Wen Shen. 2024-06-22. On the topology and geometry of certain $13$-manifolds. https://arxiv.org/abs/2406.15697

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