Yang-Hui He

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math.DG2026

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

Yang-Hui He, Ziran Liu, Shing-Tung Yau

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…

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

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