Positive sectional curvature and Ricci flow

Abstract: The preservation of positive curvature conditions under the Ricci flow has been an important ingredient in applications of the flow to solving problems in geometry and topology. Works by Hamilton and others established that certain positive curvature conditions are preserved under the flow, culminating in Wilking's unified, Lie algebraic approach to proving invariance of positive curvature conditions. Yet, some questions remain. In this talk, we describe sec > 0 initial metrics on S^4, where the condition of sec > 0 is not preserved under the Ricci flow. Previously, examples of such behaviour were known for sec \geq 0, and for sec > 0 in dimension 6 and above. This is joint work with Renato Bettiol.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.