Classification of Almost Quarter-Pinched Manifolds

TL;DR

This paper proves that simply connected manifolds with almost quarter pinched curvature are topologically equivalent to known symmetric spaces or spheres, advancing the classification of manifolds with specific curvature conditions.

Contribution

It establishes a new classification result linking almost quarter pinched curvature to well-known symmetric spaces or spheres.

Findings

Manifolds with almost quarter pinched curvature are diffeomorphic to CROSS or spheres.

Provides a classification criterion based on curvature pinching.

Enhances understanding of the topology of manifolds under curvature constraints.

Abstract

We show that if a simply connected manifold is almost quarter pinched then it is diffeomorphic to a CROSS (a compact rank one symmetric space) or a sphere.