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

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.

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

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