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Note on the Jacobi identity for Whitehead products

Published online by Cambridge University Press:  24 October 2008

P. J. Hilton
P. J. Hilton
Affiliation:
University of Birmingham
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Extract

The Jacobi identity for Whitehead products,

where α ɛ πl(X), β ɛ πm(M), γ ɛ πn (X), l, m, n ≥ 2 is now well known. In this note we extend the identity to the case l, m, n > 1; the extension is easy and we are merely filling a small gap in the literature. However, the extension does enable us to improve a result in (2).

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 1 , January 1961 , pp. 180 - 182
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Hall, M. Jr, Theory of groups (New York, 1959).Google Scholar
(2)Hilton, P. J., On a generalization of nilpotency to semi-simplicial complexes. Proc. Lond. Math. Soc. (3), 10 (1960), 604–22.CrossRefGoogle Scholar
(3)Whitehead, J. H. C., On adding relations to homotopy groups. Ann. Math. 42 (1941), 409–28.CrossRefGoogle Scholar