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Smale Theorem

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the boundaries of two closed n-balls under a suitable diffeomorphism (Milnor).

See also

Freedman Theorem, Poincaré Conjecture

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References

Milnor, J. "The Poincaré Conjecture." https://www.claymath.org/wp-content/uploads/2022/06/poincare.pdf.Smale, S. "Generalized Poincaré's Conjecture in Dimensions Greater than Four." Ann. Math. 74, 391-406, 1961.

Referenced on Wolfram|Alpha

Smale Theorem

Cite this as:

Weisstein, Eric W. "Smale Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SmaleTheorem.html

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