Elliptization conjecture: Difference between revisions
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{{topology theorem}} | {{topology theorem}} | ||
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==Statement== | ==Statement== | ||
Revision as of 05:31, 11 May 2007
This article makes a prediction about the universal cover of a manifold based on given data at the level of a:topological manifold
This result is about manifolds in dimension:3
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