Elliptization conjecture

Template:Topology theorem

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