Encyclopedia > Thurston elliptization conjecture

  Article Content

Thurston elliptization conjecture

William Thurston's Elliptization Conjecture states that a closed 3-manifold[?] with finite fundamental group has a spherical geometry, i.e. has a Riemannian metric[?] of constant positive sectional curvature. Any 3-manifold with such a metric is covered by 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.

The Elliptization Conjecture is a special case of Thurston's Geometrization Conjecture.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Rameses

... from Rameses Ramses, also spelled Rameses, is the name of several Egyptian pharaohs: Ramses I[?] Ramses II ("The Great") Ramses III Ramses IV[?] The ...

 
 
 
This page was created in 22.9 ms