THE GEOMETRIZATION CONJECTURE AFTER R. Hamilton and G. Perelman

نویسندگان

  • G. Besson
  • G. PERELMAN
چکیده

This is the text of a Lagrange Lecture given in the mathematics department of the University of Torino. It aims at describing quite briefly the main milestones in the proof of the Geometrization conjecture due to G. Perelman using R. Hamilton’s Ricci Flow. It is by no means exhaustive and intends to be a rough guide to the reading of the detailed literature on the subject. Extended notes have been published by H.-D. Cao and X.-P. Zhu ([5]), B. Kleiner and J. Lott ([16]) and J. Morgan and G. Tian ([17]). The reader may also look at the following survey papers [1, 3, 21] and the forthcoming monography [2].

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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 appr...

متن کامل

Bruce Kleiner And

These are notes on Perelman’s papers “The Entropy Formula for the Ricci Flow and its Geometric Applications” [51] and “Ricci Flow with Surgery on Three-Manifolds’ [52]. 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 appr...

متن کامل

A Complete Proof of the Poincaré and Geometrization Conjectures – Application of the Hamilton-perelman Theory of the Ricci Flow∗

In this paper, we give a complete proof of the Poincaré and the geometrization conjectures. This work depends on the accumulative works of many geometric analysts in the past thirty years. This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow.

متن کامل

Locally Collapsed 3-manifolds

We prove that a 3-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman and was used in his proof of the geometrization conjecture.

متن کامل

Geometrization of 3-Manifolds via the Ricci Flow

184 NOTICES OF THE AMS VOLUME 51, NUMBER 2 Introduction The classification of closed surfaces is a milestone in the development of topology, so much so that it is now taught to most mathematics undergraduates as an introduction to topology. Since the solution of the uniformization problem for surfaces by Poincaré and Koebe, this topological classification is now best understood in terms of the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007