In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric...

Perelman presented his work proving the Poincaré conjecture (and the more powerful geometrization conjecture of William Thurston). Over the next several years...

analysis of Ricci flow, and proved the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open problem...

the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter...

William Thurston's geometrization conjecture, Hamilton produced a number of results in the 1990s which were directed towards the conjecture's resolution. In...

conjectures, see the references in the articles on geometrization conjecture or Poincaré conjecture. William Thurston. Three-dimensional geometry and topology...

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

of results and ideas for using it to prove the Poincaré conjecture and geometrization conjecture from the field of geometric topology. Hamilton's work on...

manifolds and diffeomorphisms. A proof of this conjecture, together with the more powerful geometrization conjecture, was given by Grigori Perelman in 2002 and...

a conjecture has been proven, it is no longer a conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem...

fields to 3-manifolds. Thurston was next led to formulate his geometrization conjecture. This gave a conjectural picture of 3-manifolds which indicated...

computational methods available in surgery theory. Thurston's geometrization conjecture, formulated in the late 1970s, offered a framework that suggested...

the geometrization conjecture. Additionally, he posted a third article in which he gave a shortcut to the proof of the famous Poincaré conjecture, for...

The hypotheses of the conjecture are satisfied by hyperbolic 3-manifolds. In fact, given that the geometrization conjecture is now settled, the only...

theory of Ricci flow solve the geometrization conjecture in three-dimensional topology, of which the renowned Poincaré conjecture is a special case. Perelman's...

– (2006). "Hamilton–Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture". arXiv:math/0612069. do Carmo, Manfredo Perdigão (1992)...

After the proof of the geometrization conjecture by Perelman, the conjecture was only open for hyperbolic 3-manifolds. The conjecture is usually attributed...

Spherical space form conjecture (Grigori Perelman, 2006) Poincaré conjecture (Grigori Perelman, 2002) Geometrization conjecture, (Grigori Perelman, series...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

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

in Grigori Perelman's proof of the Geometrization conjecture, which included the proof of the Poincaré conjecture, a Millennium Prize Problem. Geometric...

Poincaré Conjecture, Richard S. Hamilton's formulation of a strategy to prove the conjecture, and William Thurston's geometrization conjecture. Yau's long...

decomposition is not quite the same as the decomposition in the geometrization conjecture, because some of the pieces in the JSJ decomposition might not...

Thurston's geometrization theorem also follows from Perelman's proof using Ricci flow of the more general Thurston geometrization conjecture. Thurston's...

latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman...

compact oriented manifolds in 6 of the 8 Thurston geometries of the geometrization conjecture. A Seifert manifold is a closed 3-manifold together with a decomposition...

zero curvature/flat, and negative curvature/hyperbolic – and the geometrization conjecture (now theorem) in 3 dimensions – every 3-manifold can be cut into...

geometry, geometrization theorem may refer to Thurston's hyperbolization theorem for Haken 3-manifolds Thurston's geometrization conjecture proved by...

spaces such as Jacob's ladder. In dimension 3, William Thurston's geometrization conjecture, proven by Grigori Perelman, gives a partial classification of...

theorem for 3-manifolds, the capstone of his proof of Thurston's geometrization conjecture, can be understood as an extension of the implicit function theorem...