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arXiv · 2610.33474

Hitchin's $α$-invariant and positive sectional curvature on homotopy $9$-spheres

Yang-Hui He·Ziran Liu·Shing-Tung Yau
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Abstract

We prove that a smooth homotopy $9$-sphere admits a Riemannian metric of positive sectional curvature if and only if its Hitchin $α$-invariant vanishes, or equivalently if and only if it admits a Riemannian metric of positive scalar curvature.

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Yang-Hui He, Ziran Liu, Shing-Tung Yau. 2026-10-24. Hitchin's $α$-invariant and positive sectional curvature on homotopy $9$-spheres. https://arxiv.org/abs/2610.33474

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