Geometrization theorem
Encyclopedia
In geometry, geometrization theorem may refer to
- Thurstons's hyperbolization theoremHyperbolization theoremIn geometry, Thurston's geometrization theorem or hyperbolization theorem implies that closed atoroidal Haken manifolds are hyperbolic, and in particular satisfy the Thurston conjecture.-Statement:...
for Haken 3-manifolds - Thurston's geometrization conjectureGeometrization conjectureThurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces...
proved by Perelman, a generalization of the hyperbolization theorem to all compact 3-manifolds.