Some applications of Ricci flow to 3-manifolds

TL;DR

This paper introduces Ricci flow techniques and their applications to the geometry and topology of 3-manifolds, including geometrization, surgery, and scalar curvature obstructions, aimed at nonexperts.

Contribution

It provides an accessible overview of Ricci flow with surgery and its role in understanding 3-manifold geometrization, including new results on open manifolds and scalar curvature.

Findings

Introduction to Ricci flow with surgery

Results on geometrization of 3-manifolds

Obstructions to positive scalar curvature

Abstract

We decribe and announce some results (joint with G. Besson, L. Bessieres, M. Boileau and J.Porti) about the geometry and topology of 3-manifolds. Most of the article is primarily intended as an introduction for nonexperts to geometrization of 3-manifolds, Ricci flow with surgery, and the simplicial volume approach to collapsing theorems. In the last section, Ricci flow with surgery on open 3-manifolds and obstructions to positive scalar curvature are discussed.