Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture

2006/12/03 by Huai-Dong Cao, Cao, Huai-Dong, Xi-Ping Zhu +1
Mathematics · #53C21 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C21 #msc:53C44

paper · pdf · doi:10.48550/arxiv.math/0612069

This is a revised version of the article by the same authors that originally appeared in Asian J. Math., {\bf 10}({\bf 2}) (2006), 165--492

arxiv created 2006/12/03 · arxiv updated 2009/12/01

Abstract

In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In particular, we give a detailed exposition of a complete proof of the Poincaré conjecture due to Hamilton and Perelman.

Related

• Perelman, Poincare, and the Ricci Flow
• Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective
• A Survey of Hamilton's Program for the Ricci Flow on 3-manifolds
• Completion of the Proof of the Geometrization Conjecture
• Ricci flow on Poincare' and Thurston's Geometrization Conjecture