Thurston Elliptization Conjecture

Every closed three-manifold with finite fundamental group has a metric of constant positive scalar curvature, and hence is homeomorphic to a quotient S^3/Gamma, where Gamma subset SO(4) is a finite group of rotations that acts freely on S^3.

Since the trivial group is in particular a finite group, the elliptization conjecture implies the Poincaré conjecture.

See also

Poincaré Conjecture, Thurston's Geometrization Conjecture

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Anderson, M. T. "Scalar Curvature and Geometrization Conjectures for 3-Manifolds." MSRI Publ. 30, 1997., J. "The Poincaré Conjecture.", J. Collected Papers, Vol. 2: The Fundamental Group. Publish or Perish Press, p. 93, 1995.

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Thurston Elliptization Conjecture

Cite this as:

Weisstein, Eric W. "Thurston Elliptization Conjecture." From MathWorld--A Wolfram Web Resource.

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