On some new Ricci flow invariant curvature conditions

TL;DR

This paper investigates new curvature conditions invariant under Ricci flow, providing evidence for a conjecture and exploring implications for the topology of manifolds with specific curvature pinching.

Contribution

It introduces new Ricci flow invariant curvature conditions and offers quantitative support for an unpublished conjecture by B"ohm and Wilking.

Findings

Evidence supporting B"ohm and Wilking's conjecture

Analysis of topology of manifolds with pinched curvature

Introduction of new invariant curvature conditions

Abstract

We would like to study new Ricci flow invariant curvature conditions. Specifically, we provide quantitative evidence for an unpublished conjecture of B\"ohm and Wilking. As an application, we study the topology of manifolds with pinched curvature.