Long-time behavior of $3$–dimensional Ricci flow: introduction

Abstract

In the following series of papers we analyze the long-time behavior of $3$–dimensional Ricci flows with surgery. Our main result will be that if the surgeries are performed correctly, then only finitely many surgeries occur and after some time the curvature is bounded by $C{t}^{-1}$. This result confirms a conjecture of Perelman. In the course of the proof, we also obtain a qualitative description of the geometry as $t\to \infty$.