#### Volume 22, issue 2 (2018)

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

### Richard H Bamler

Geometry & Topology 22 (2018) 757–774
##### 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 $t\to \infty$.

##### Keywords
Ricci flow, Ricci flow with surgery, finitely many surgeries, asymptotics of Ricci flow, $3$–manifolds, geometrization of $3$–manifolds
##### Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 49Q05, 53C23, 57M15, 57M20, 57M50