Hitchin's -invariant and positive sectional curvature on homotopy -spheres
arXiv:2610.33474
Abstract
We prove that a smooth homotopy -sphere admits a Riemannian metric of positive sectional curvature if and only if its Hitchin -invariant vanishes, or equivalently if and only if it admits a Riemannian metric of positive scalar curvature.
arXiv comment44 pages