3-spheres are unique 3-manifolds {Poincaré conjecture} [1904]. If all loops in three-dimensional compact closed space can shrink to points, without breaking loop or space, space is 3-sphere, and no other such 3-space exists. 4-spheres are unique 4-manifolds, as proved by Michael Freedman [1983]. 5-spheres are unique 5-manifolds, and all higher dimensional spheres are unique manifolds, as proved by Stephen Smale [1960].
Mathematical Sciences>Topology>Surface>Manifold
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Date Modified: 2022.0224