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Summary Of: Poincaré conjecture

The Poincaré conjecture claims that if such a space has the additional property that each... The Poincaré conjecture asks the same question for the 3... The Poincaré conjecture asks the same question for the 3... The Poincaré conjecture remains the only solved Millennium problem... s proof of the Poincaré conjecture as the scientific... shocked mathematicians by proving the Generalized Poincaré conjecture for dimensions greater than four and extended his techniques to prove the fundamental... The Poincaré conjecture was essentially true in both dimension four and all higher dimensions for substantially different reasons... consensus among the experts as to whether the Poincaré conjecture was true or false... these papers he sketched a proof of the Poincaré conjecture and a more general conjecture... s program for proving the Poincaré conjecture involves first putting a... This easily implies the Poincaré conjecture in the case of positive Ricci curvature... This result implies the Poincaré conjecture because it is easy to check it for the possible manifolds listed in the conclusion... Recent progress on the Poincaré conjecture and the classification of 3... The Poincaré Conjecture 99 Years Later... s Proof of the Poincaré Conjecture and the Geometrization Conjecture...

Encyclodia Page On: Poincaré conjecture

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mathematics | [pwɛ̃kaʀe] | theorem | characterization | three-dimensional sphere | three-dimensional manifolds | conjecture | Fields medal | closed | 3-manifold | loop | | | Grigori Perelman | Richard Hamilton | topology | Millennium Prize Problems | Clay Mathematics Institute | Fields Medal | December 22 | 2006 | Science | Breakthrough of the Year | Millennium Prize Problems | P versus NP | The Hodge conjecture | The Riemann hypothesis | Yang–Mills existence and mass gap | Navier–Stokes existence and smoothness | The Birch and Swinnerton-Dyer conjecture | Henri Poincaré | combinatorial topology | algebraic topology | sphere | homology | Enrico Betti | 3-manifold | Poincaré homology sphere | homology sphere | topological invariant | fundamental group | fundamental group | simply connected | compact | manifold | homeomorphic | Generalized Poincaré conjecture | classification of closed surfaces | Stephen Smale | h-cobordism theorem | Michael Freedman | geometrization conjecture | John Morgan | Thurston | hyperbolic 3-manifolds | J. H. C. Whitehead | Whitehead manifold | Bing | Haken | Moise | Papakyriakopoulos | John Milnor | peer-reviewed | Solution of the Poincaré conjecture | Ricci flow | Grigori Perelman | Steklov Institute of Mathematics | Saint Petersburg | arXiv | Thurston's geometrization conjecture | Richard Hamilton | Bruce Kleiner | Huai-Dong Cao | Xi-Ping Zhu | John Morgan | Gang Tian | August 22 | 2006 | ICM | Fields Medal | August 24 | 2006 | The New Yorker | Manifold Destiny | Science | Ricci flow | Riemannian metric | Ricci flow | free product | finite groups | cyclic groups | graph manifold | ISBN 0-395-82517-2 | 2007 | 05-05 | doi | Bing, RH | Milnor, John | 9 April | 2002 | Hamilton, Richard | ISBN 978-1571461100 | Perelman, Grigori | arΧiv | arΧiv | arΧiv | Kleiner, Bruce | John Lott | arΧiv | Cao, Huai-Dong | Xi-Ping Zhu | PDF | arΧiv | Morgan, John | Gang Tian | arΧiv | Morgan, John | Gang Tian | ISBN 0821843281 | Nasar, Sylvia | August 28 | 2006 | Manifold destiny | The New Yorker | August 22 | 2006 | New York Times | China Daily | 23 August | 2006 | Terence Tao | arΧiv | 25 August | 2006 | BBC Radio 4 | In Our Time | Open University | Ian Stewart | University of Warwick | Marcus du Sautoy | University of Oxford | Melvyn Bragg | 21 August | 2006 | The New Yorker | Categories | Geometric topology | 3-manifolds | Conjectures | Millennium Prize Problems | Surgery theory |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Poincaré conjecture".