Highly connected 7-manifolds and non-negative curvature

Abstract

In this article, a six-parameter family of highly connected 7-manifolds which admit an 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 SO(3)-invariant metric of non-negative curvature.

62 pages; Final Version. To appear in Ann. of Math

References in corpus (2)

• An exotic sphere with positive sectional curvature
• The classification of 2-connected 7-manifolds

Cited by in corpus (3)

• On the geometry of some Equivariantly related manifolds
• On the moduli space of nonnegatively curved metrics on Milnor spheres
• Highly connected 7-manifolds, the linking form and non-negative curvature