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
Anna Karenina

... Contents Anna Karenina Anna Karenina is a novel by Leo Tolstoy published in 1877 through 1878, set against the background of Russian society of that time. Its theme is ...

 
 
 
This page was created in 31.2 ms