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This is a Quantitative Study study.

October 5, 2025Open Access

Classification for smooth manifolds looking like CP³ S⁷

Key Points

Simply connected closed 13-dimensional manifolds showed similarity to the structure of CP^3×S^7, indicating deeper geometrical properties.
Cohomology ring isomorphism was established in the context of diffeomorphism and homotopy equivalence classifications.
Certain manifolds from this classification allow for non-negative sectional curvature under specific conditions, influencing geometrical understanding.
Diagonal S^1-actions on S^7×S^7 were classified, providing insight into symmetries within these manifolds.

Abstract

In this paper, we classify simply connected closed smooth 13-dimensional manifolds whose cohomology ring is isomorphic to that of CP³ S⁷, 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 S¹-actions on S⁷ S⁷.

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Wen Zhong Shen (Wed,) studied this question.

www.synapsesocial.com/papers/68e25378d6d66a53c2474103 — DOI: https://doi.org/10.48550/arxiv.2510.00613

Classification for smooth manifolds looking like CP³ S⁷

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