Manifolds with almost nonnegative curvature operator and principal bundles

TL;DR

This paper investigates manifolds with almost nonnegative curvature operator, providing the first examples of simply connected closed manifolds with ANCO that do not admit nonnegative curvature operator.

Contribution

It introduces the first known examples of simply connected closed manifolds with ANCO lacking nonnegative curvature operator.

Findings

First examples of simply connected ANCO manifolds without nonnegative curvature operator

Demonstrates the distinction between ANCO and nonnegative curvature operator

Advances understanding of curvature conditions on manifolds

Abstract

We study manifolds with almost nonnegative curvature operator (ANCO) and provide first examples of closed simply connected ANCO mannifolds that do not admit nonnegative curvature operator.