Every closed three-manifold with finite fundamental group has a metric of constant positive scalar
curvature , and hence is homeomorphic to a quotient
,
where
is a finite group of rotations that acts freely on .

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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References Anderson, M. T. "Scalar Curvature and Geometrization Conjectures for 3-Manifolds." MSRI Publ. 30, 1997. http://www.math.sunysb.edu/~anderson/papers.html . Milnor,
J. "The Poincaré Conjecture." http://www.claymath.org/millennium/Poincare_Conjecture/Official_Problem_Description.pdf . Milnor,
J. Collected
Papers, Vol. 2: The Fundamental Group. Publish or Perish Press, p. 93,
1995. Referenced on Wolfram|Alpha Thurston Elliptization
Conjecture
Cite this as:
Weisstein, Eric W. "Thurston Elliptization Conjecture." From MathWorld --A Wolfram Web Resource.
https://mathworld.wolfram.com/ThurstonElliptizationConjecture.html

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