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The Hopf invariant and homotopy groups of spheres

Published online by Cambridge University Press:  24 October 2008

P. J. Hilton
P. J. Hilton
Affiliation:
Victoria UniversityManchester
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Extract

In (5), Whitehead introduced a generalization of the Hopfinvariant in the form of a homomorphism H: πr(Sn) → πr(S2n−1), valid† if r < 3n − 3. In (2), the author extended Whitehead's definition to cover the cases r ≤ 4n − 4; r = 5, n = 2; r = 13, n = 4. He also defined, without restriction, a homomorphism

which was related to H, whenever H was defined, by the equation H* = FH, F being the Freudenthal suspension

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 4 , October 1952 , pp. 547 - 554
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Blakers, A. L. and Massey, W. S.The homotopy groups of a triad, I. Ann. Math., Princeton (2), 53 (1951), 161–205.CrossRefGoogle Scholar
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