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- Geometrization_conjecture abstract "In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply-connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic).In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston (1982), and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's hyperbolization theorem implies that Haken manifolds satisfy the geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print.Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery.There are now several different manuscripts (see below) with details of the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.".
- Geometrization_conjecture wikiPageExternalLink 0211159.
- Geometrization_conjecture wikiPageExternalLink 0303109.
- Geometrization_conjecture wikiPageExternalLink 0307245.
- Geometrization_conjecture wikiPageExternalLink 0605667.
- Geometrization_conjecture wikiPageExternalLink 0612069.
- Geometrization_conjecture wikiPageExternalLink threemanifolds.
- Geometrization_conjecture wikiPageExternalLink book.pdf.
- Geometrization_conjecture wikiPageExternalLink item=CMIM-5.
- Geometrization_conjecture wikiPageExternalLink item=ulect-53.
- Geometrization_conjecture wikiPageExternalLink S0273-0979-04-01045-6.pdf.
- Geometrization_conjecture wikiPageExternalLink Quadern25-1.pdf.
- Geometrization_conjecture wikiPageExternalLink AJM-10-2-165-492-Abstract.php.
- Geometrization_conjecture wikiPageExternalLink 3M.pdf.
- Geometrization_conjecture wikiPageExternalLink 8geoms.pdf.
- Geometrization_conjecture wikiPageExternalLink errata8geoms.pdf.
- Geometrization_conjecture wikiPageExternalLink gt3m.
- Geometrization_conjecture wikiPageID "220642".
- Geometrization_conjecture wikiPageRevisionID "606228452".
- Geometrization_conjecture authorlink "William Thurston".
- Geometrization_conjecture first "William".
- Geometrization_conjecture hasPhotoCollection Geometrization_conjecture.
- Geometrization_conjecture last "Thurston".
- Geometrization_conjecture year "1982".
- Geometrization_conjecture subject Category:3-manifolds.
- Geometrization_conjecture subject Category:Conjectures.
- Geometrization_conjecture subject Category:Geometric_topology.
- Geometrization_conjecture subject Category:Riemannian_geometry.
- Geometrization_conjecture type Abstraction100002137.
- Geometrization_conjecture type Cognition100023271.
- Geometrization_conjecture type Concept105835747.
- Geometrization_conjecture type Conjectures.
- Geometrization_conjecture type Content105809192.
- Geometrization_conjecture type Hypothesis105888929.
- Geometrization_conjecture type Idea105833840.
- Geometrization_conjecture type PsychologicalFeature100023100.
- Geometrization_conjecture type Speculation105891783.
- Geometrization_conjecture comment "In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply-connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic).In three dimensions, it is not always possible to assign a single geometry to a whole topological space.".
- Geometrization_conjecture label "Congettura di geometrizzazione di Thurston".
- Geometrization_conjecture label "Geometrisierung von 3-Mannigfaltigkeiten".
- Geometrization_conjecture label "Geometrization conjecture".
- Geometrization_conjecture label "Géométrisation des 3-variétés".
- Geometrization_conjecture label "Vermeetkundigingsvermoeden van Thurston".
- Geometrization_conjecture label "Гипотеза Тёрстона".
- Geometrization_conjecture label "几何化猜想".
- Geometrization_conjecture label "幾何化予想".
- Geometrization_conjecture sameAs Geometrisierung_von_3-Mannigfaltigkeiten.
- Geometrization_conjecture sameAs Géométrisation_des_3-variétés.
- Geometrization_conjecture sameAs Congettura_di_geometrizzazione_di_Thurston.
- Geometrization_conjecture sameAs 幾何化予想.
- Geometrization_conjecture sameAs 기하화_추측.
- Geometrization_conjecture sameAs Vermeetkundigingsvermoeden_van_Thurston.
- Geometrization_conjecture sameAs m.01g72p.
- Geometrization_conjecture sameAs Q1503309.
- Geometrization_conjecture sameAs Q1503309.
- Geometrization_conjecture sameAs Geometrization_conjecture.
- Geometrization_conjecture wasDerivedFrom Geometrization_conjecture?oldid=606228452.
- Geometrization_conjecture isPrimaryTopicOf Geometrization_conjecture.