Elliptization conjecture

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Template:Topology theorem

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