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.

Authors

Sebastian Goette

Mathematisches Institut, Universität Freiburg, Germany

Martin Kerin

School of Mathematics, Statistics and Applied Mathematics, NUI Galway, Ireland

Krishnan Shankar

Department of Mathematics, The University of Oklahoma, Norman, OK, USA