An Algebraic Identity for Curvature Operators

Abstract

In this chapter and the next we look at one of the most important recent developments in the theory of Ricci flow: The work of Böhm and Wilking [BW08] which gives a method for producing whole families of preserved convex sets for the Ricci flow from a given one. This remarkable new method has broken through what was an enormous barrier to further applications of Ricci flow: In particular the proof of the differentiable sphere theorem relies heavily on this work. Show more