In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about...

the Poincaré Conjecture and the Geometrization Conjecture". arXiv:math.DG/0612069. Morgan, John W.; Tian, Gang Ricci Flow and the Poincaré Conjecture arXiv:math/0607607...

for solving the Poincare conjecture, though Perelman declined both awards. The Poincaré conjecture and the spherical space form conjecture are corollaries...

Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official...

In the mathematical area of topology, the generalized Poincaré conjecture is a statement that a manifold which is a homotopy sphere is a sphere. More...

important 3-manifold because of the now-proven Poincaré conjecture. Originally conjectured by Henri Poincaré, the theorem concerns a space that locally looks...

Poincaré conjecture), Fermat's Last Theorem, and others. Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf...

equivalent to two simpler conjectures: the Poincaré conjecture and the spherical space form conjecture. The elliptization conjecture is a special case of Thurston's...

mechanics. The Poincaré group used in physics and mathematics was named after him. Early in the 20th century he formulated the Poincaré conjecture, which became...

popularized the name and conjecture. This conjecture can be thought of as a first step to resolving the Poincaré conjecture, since the Lickorish–Wallace...

smooth Poincaré conjecture is known in all dimensions other than 4 (it is usually false in dimensions at least 7; see exotic sphere). The Poincaré conjecture...

counterexample to the Poincaré Conjecture, if one existed. In 2002, Martin Dunwoody posted a claimed proof of the Poincaré Conjecture. Rourke identified...

More specifically, the conjecture states that certain de Rham cohomology classes are algebraic; that is, they are sums of Poincaré duals of the homology...

claiming a resolution of the renowned Poincaré conjecture, along with the more general geometrization conjecture. His work contained a number of notable...

proving the Poincaré and geometrization conjectures in 2003. Perelman was awarded a Millennium Prize for resolving the Poincaré conjecture but declined...

Thurston conjecture and the Poincaré conjecture, regarded as a special case of the former. It should be emphasized that the Poincare conjecture has been...

made regarding his work habits while proving the higher-dimensional Poincaré conjecture. He said that his best work had been done "on the beaches of Rio...

awarded a Fields Medal for his work on the 4-dimensional generalized Poincaré conjecture. Freedman and Robion Kirby showed that an exotic R4 manifold exists...

generalization of the Poincaré conjecture to the non-simply connected case. The conjecture is implied by Thurston's geometrization conjecture, which was proven...

nearly a century, Grigori Perelman proved the Poincaré conjecture (see the Solution of the Poincaré conjecture). William Thurston's geometrization program...

smooth Poincaré conjecture is known in all dimensions other than 4 (it is usually false in dimensions at least 7; see exotic sphere). The Poincaré conjecture...

dimension 3 (the original Poincaré conjecture) by Grigori Perelman in 2005. The resolution of the smooth Poincaré conjecture in dimensions 5 and larger...

Poincaré theorem may refer to: Poincaré conjecture, on homeomorphisms to the sphere; Poincaré recurrence theorem, on sufficient conditions for recurrence...

be measured. The seven problems are: P versus NP The Hodge conjecture The Poincaré conjecture - solved, by Grigori Perelman The Riemann hypothesis Yang-Mills...

homotopy n-spheres are homeomorphic to the n-sphere by the generalized Poincaré conjecture, proved by Stephen Smale in dimensions bigger than 4, Michael Freedman...

mathematicians) of some of the circumstances surrounding the proof of the Poincaré conjecture, one of the most important accomplishments of 20th and 21st century...

mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to...

the Poincaré conjecture, was solved by Grigori Perelman in 2003. However, a generalization called the smooth four-dimensional Poincaré conjecture—that...

conjecture has been proved for dimensions 1 and 2, and it is known that the 3-dimensional version of the conjecture implies the Poincaré conjecture....

theorem Poincaré algebra K-Poincaré algebra Super-Poincaré algebra Poincaré–Bjerknes circulation theorem Poincaré complex Poincaré conjecture, one of...