Year: 2025
Type: preprint
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 $Σ^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-actions on $S^7\times S^7$.
Source: arXiv (Cornell University)
Author: Shen, Wen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414808548
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