gave a proof in the case of manifolds that fiber over the circle, and  and  gave proofs for the generic case of manifolds that do not fiber over the circle. Thurston's geometrization theorem also follows from Perelman's proof using Ricci flow of the more general Thurston geometrization conjecture.
provided evidence in the case of manifolds that fiber over the circle,  and  provided proofs for the generic case of manifolds that do not fiber over the circle. Thurston's geometrization theorem also stems from Perelman's proof using Ricci flow of the more general Thurston geometrization conjecture.