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![]() Perelman's solution was based on Richard Hamilton's theory of Ricci flow. ![]() The precise formulation of the conjecture states:Įvery simply connected, closed 3-manifold is homeomorphic to the 3-sphere.Ī proof of this conjecture was given by Grigori Perelman in 2003. It is central to the more general problem of classifying all 3-manifolds. The Poincaré conjecture states that this is also true in dimension 3. In dimension 2, a sphere is characterized by the fact that it is the only closed and simply-connected surface.
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