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 , 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.

REFERENCES:

Anderson, M. T. "Scalar Curvature and Geometrization Conjectures for 3-Manifolds." MSRI Publ. 30, 1997. https://www.math.sunysb.edu/~anderson/papers.html.

Milnor, J. "The Poincaré Conjecture." https://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.