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Homotopy Sphere


An n-dimensional manifold M is said to be a homotopy sphere, if it is homotopy equivalent to the n-sphere S^n. Thus no homotopy group can distinguish between M and S^n.

The solution of the generalized Poincaré conjecture in the positive implies that any compact homotopy sphere is in fact homeomorphic to a sphere.


This entry contributed by Rasmus Hedegaard

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Cite this as:

Hedegaard, Rasmus. "Homotopy Sphere." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HomotopySphere.html

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