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- Thurston_elliptization_conjecture abstract "William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of constant positive sectional curvature. A 3-manifold with such a metric is covered by the 3-sphere, moreover the group of covering transformations are isometries of the 3-sphere. Note that this means that if the original 3-manifold had in fact a trivial fundamental group, then it is homeomorphic to the 3-sphere (via the covering map). Thus, proving the elliptization conjecture would prove the Poincaré conjecture as a corollary. In fact, the elliptization conjecture is logically equivalent to two simpler conjectures: the Poincaré conjecture and the spherical space form conjecture.The elliptization conjecture is a special case of Thurston's geometrization conjecture, which was proved in 2003 by G. Perelman.".
- Thurston_elliptization_conjecture wikiPageExternalLink gt3m.
- Thurston_elliptization_conjecture wikiPageID "235954".
- Thurston_elliptization_conjecture wikiPageLength "1677".
- Thurston_elliptization_conjecture wikiPageOutDegree "19".
- Thurston_elliptization_conjecture wikiPageRevisionID "577000038".
- Thurston_elliptization_conjecture wikiPageWikiLink 3-sphere.
- Thurston_elliptization_conjecture wikiPageWikiLink Category:3-manifolds.
- Thurston_elliptization_conjecture wikiPageWikiLink Category:Conjectures.
- Thurston_elliptization_conjecture wikiPageWikiLink Category:Riemannian_geometry.
- Thurston_elliptization_conjecture wikiPageWikiLink Covering_space.
- Thurston_elliptization_conjecture wikiPageWikiLink Fundamental_group.
- Thurston_elliptization_conjecture wikiPageWikiLink Geometrization_conjecture.
- Thurston_elliptization_conjecture wikiPageWikiLink Grigori_Perelman.
- Thurston_elliptization_conjecture wikiPageWikiLink Homeomorphism.
- Thurston_elliptization_conjecture wikiPageWikiLink Logical_equivalence.
- Thurston_elliptization_conjecture wikiPageWikiLink Manifold.
- Thurston_elliptization_conjecture wikiPageWikiLink Poincaré_conjecture.
- Thurston_elliptization_conjecture wikiPageWikiLink Riemannian_manifold.
- Thurston_elliptization_conjecture wikiPageWikiLink Spherical_3-manifold.
- Thurston_elliptization_conjecture wikiPageWikiLink Spherical_space_form_conjecture.
- Thurston_elliptization_conjecture wikiPageWikiLink William_Thurston.
- Thurston_elliptization_conjecture wikiPageWikiLinkText "Thurston elliptization conjecture".
- Thurston_elliptization_conjecture wikiPageWikiLinkText "elliptization conjecture".
- Thurston_elliptization_conjecture subject Category:3-manifolds.
- Thurston_elliptization_conjecture subject Category:Conjectures.
- Thurston_elliptization_conjecture subject Category:Riemannian_geometry.
- Thurston_elliptization_conjecture hypernym I.
- Thurston_elliptization_conjecture type Person.
- Thurston_elliptization_conjecture type Conjecture.
- Thurston_elliptization_conjecture type Redirect.
- Thurston_elliptization_conjecture type Statement.
- Thurston_elliptization_conjecture type Statement.
- Thurston_elliptization_conjecture comment "William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of constant positive sectional curvature. A 3-manifold with such a metric is covered by the 3-sphere, moreover the group of covering transformations are isometries of the 3-sphere. Note that this means that if the original 3-manifold had in fact a trivial fundamental group, then it is homeomorphic to the 3-sphere (via the covering map).".
- Thurston_elliptization_conjecture label "Thurston elliptization conjecture".
- Thurston_elliptization_conjecture sameAs Q13605872.
- Thurston_elliptization_conjecture sameAs Elliptisatievermoeden_van_Thurston.
- Thurston_elliptization_conjecture sameAs m.01j836.
- Thurston_elliptization_conjecture sameAs Q13605872.
- Thurston_elliptization_conjecture wasDerivedFrom Thurston_elliptization_conjecture?oldid=577000038.
- Thurston_elliptization_conjecture isPrimaryTopicOf Thurston_elliptization_conjecture.