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A certain triple Whitehead product

Published online by Cambridge University Press:  24 October 2008

P. J. Hilton
P. J. Hilton
Affiliation:
Pembroke CollegeCambridge
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Extract

The triple Whitehead product we consider in this note is [[ɩn, ɩn], ɩn] ∈ π3n−2(Sn), where ɩn generates πn(Sn). It follows from the Jacobi identity for Whitehead products

α ∈ πp(X), β ∈ πq(X), γ ∈ πr(X), that 3[[ɩn, ɩn], ɩn] = 0. Now, if n is odd, 2[ɩn, ɩn] = 0, so that 2[[ɩn, ɩn], ɩn] = 0, whence

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 189 - 197
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

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