Elliptization conjecture: Difference between revisions

Revision as of 05:15, 11 May 2007

This article makes a prediction about the universal cover of a manifold based on given data at the level of a:[[{{{1}}}]][[Category: Results predicting the universal cover at the level of {{{1}}}]]

Statement

Verbal statement

Any closed 3-manifold with finite fundamental group is spherical, viz it has a Riemannian metirc with positive sectional curvature (or equivalently, its universal cover is the 3-sphere).

Relation with other results

Weaker results

Poincare conjecture: In the particular case that the fundamental group is trivial, this actually tells us that the manifold is homeomorphic to the 3-sphere

@@ Line 1: / Line 1: @@
-#REDIRECT [[Geometrization conjecture]]
+{{topology theorem}}
+{{universal cover prediction}}
+==Statement==
+===Verbal statement===
+Any closed 3-manifold with finite fundamental group is [[spherical manifold|spherical]], viz it has a Riemannian metirc with positive sectional curvature (or equivalently, its universal cover is the 3-sphere).
+==Relation with other results==
+===Weaker results===
+* [[Poincare conjecture]]: In the particular case that the fundamental group is trivial, this actually tells us that the manifold is homeomorphic to the 3-sphere