Highly connected $7$-manifolds and non-negative sectional curvature

Abstract

In this article, a six-parameter family of highly connected 7-manifolds which admit an $\mathrm {SO}(3)$-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an $\mathrm{SO}(3)$-invariant metric of non-negative curvature.