An exotic sphere with positive sectional curvature

TL;DR

This paper demonstrates the existence of a metric with positive sectional curvature on the Gromoll-Meyer sphere, contributing to the understanding of curvature properties of exotic spheres.

Contribution

It constructs a specific metric on the Gromoll-Meyer sphere that exhibits positive sectional curvature, a novel result in differential geometry.

Findings

Existence of positive sectional curvature metric on Gromoll-Meyer sphere

Advances understanding of curvature on exotic spheres

Provides new examples in Riemannian geometry

Abstract

We show that there is a metric on the Gromoll-Meyer sphere with positive sectional curvature.