Ricci Flow and the Poincaré Conjecture


CMIM/3 For over 100 years the Poincaré Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. In 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincaré Conjecture in the affirmative.

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@inproceedings{Morgan2007RicciFA, title={Ricci Flow and the Poincar{\'e} Conjecture}, author={John Morgan and Conrad I. Daubechies and Charles Fefferman}, year={2007} }