On Perelman ’ S Papers

These are notes on Perelman’s papers “The Entropy Formula for the Ricci Flow and its Geometric Applications” [40] and “Ricci Flow with Surgery on Three-Manifolds’ [41]. In these two remarkable preprints, which were posted on the ArXiv in 2002 and 2003, Grisha Perelman announced a proof of the Poincaré Conjecture, and more generally Thurston’s Geometrization Conjecture, using the Ricci flow approach of Hamilton. Perelman’s proofs are concise and, at times, sketchy. The purpose of these notes is to provide the details that are missing in [40] and [41], which contain Perelman’s arguments for the Geometrization Conjecture.