Geometrization conjecture

Three dimensional analogue of uniformization conjecture Geometrization theoremFieldGeometric topologyConjectured byWilliam ThurstonConjectured in1982First proof byGrigori PerelmanFirst proof in2003ConsequencesPoincaré conjectureThurston elliptization conjecture William Thurston (pictured) proposed this conjecture in 1982 In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston (1982) as part of his 24 questions, and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptiz