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- Q13605872 subject Q6248542.
- Q13605872 subject Q7210663.
- Q13605872 subject Q8981903.
- Q13605872 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.".
- Q13605872 wikiPageExternalLink gt3m.
- Q13605872 wikiPageWikiLink Q117346.
- Q13605872 wikiPageWikiLink Q1503309.
- Q13605872 wikiPageWikiLink Q16969147.
- Q13605872 wikiPageWikiLink Q202906.
- Q13605872 wikiPageWikiLink Q203586.
- Q13605872 wikiPageWikiLink Q203920.
- Q13605872 wikiPageWikiLink Q220433.
- Q13605872 wikiPageWikiLink Q2274197.
- Q13605872 wikiPageWikiLink Q332648.
- Q13605872 wikiPageWikiLink Q333927.
- Q13605872 wikiPageWikiLink Q6248542.
- Q13605872 wikiPageWikiLink Q632814.
- Q13605872 wikiPageWikiLink Q662830.
- Q13605872 wikiPageWikiLink Q7210663.
- Q13605872 wikiPageWikiLink Q7576696.
- Q13605872 wikiPageWikiLink Q8981903.
- Q13605872 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).".
- Q13605872 label "Thurston elliptization conjecture".