Homotopy sphere

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In algebraic topology, a branch of mathematics, a homotopy sphere is a n-manifold homotopy equivalent to an n-sphere. It thus has the same homotopy groups and the same homology groups, as a sphere. So every homotopy sphere is an homology sphere.

The generalized Poincaré conjecture is that any homotopy sphere is a sphere; see the article Poincaré conjecture for more details.

See also