Highly connected 7-manifolds and non-negative curvature

2017/05/16 by Goette, Sebastian, Kerin, Martin, Shankar, Krishnan
#57R55 #58J28 #Differential Geometry (math.DG) #FOS: Mathematics #primary: 53C20 #secondary: 57R20

paper · doi:10.48550/arxiv.1705.05895

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.

Related

• Highly connected 7-manifolds, the linking form and non-negative\n curvature
• An exotic sphere with positive curvature
• Moduli spaces of nonnegatively curved metrics on exotic spheres
• Non-negatively curved 6-manifolds with almost maximal symmetry rank
• Seven dimensional cohomogeneity one manifolds with nonnegative curvature