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 .
Thurston Elliptization Conjecture
See alsoPoincaré Conjecture, Thurston's Geometrization Conjecture
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ReferencesAnderson, 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.
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Cite this as:
Weisstein, Eric W. "Thurston Elliptization Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThurstonElliptizationConjecture.html