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Hopf Invariant One Theorem


The Hopf invariant one theorem, sometimes also called Adams' theorem, is a deep theorem in homotopy theory which states that the only n-spheres which are H-spaces are S^0, S^1, S^3, and S^7. The theorem was proved by Adams (1958, 1960).


See also

H-Space, Homotopy

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References

Adams, J. F. "On the Nonexistence of Elements of Hopf Invariant One." Bull. Amer. Math. Soc. 64, 279-282, 1958.Adams, J. F. "On the Nonexistence of Elements of Hopf Invariant One." Ann. Math. 72, 20-104, 1960.

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Hopf Invariant One Theorem

Cite this as:

Weisstein, Eric W. "Hopf Invariant One Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HopfInvariantOneTheorem.html

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