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A Note on the Homotopy-Commutativity of Suspensions

Published online by Cambridge University Press:  20 November 2018

C.S. Hoo
C.S. Hoo*
Affiliation:
University of Alberta Edmonton, Alberta
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Let A and X be spaces. Then as is wellknown, [∑A, X] is a group where ∑ denotes the suspension. We wish to find conditions on A which will imply that this group is abelian for all spaces X, that is, ∑A is homotopy-commutative. This is equivalent to saying that conii A≤ 1 (see [2] for definition). Our results contain relations between conil A and the generalised Whitehead product of [1]. We work in the category of complexes with base points.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 5 , December 1967 , pp. 665 - 668
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Arkowitz, M., The generalised Whitehead product. Pac. J. Math. 12 (1966) 7-23.Google Scholar
2. Berstein, I. and Ganea, T., Homotopicalnilpotency. I 11. J. Math. 5 (1966) 99-130.Google Scholar
3. Berstein, I. and Hilton, P. J., On suspensions and comultiplications. Topology 2 (1966) 73-82.Google Scholar
4. Ganea, T., On some numerical homotopy invariants, Proc. International Congress of Mathematicians (1966) 467-472.Google Scholar
5. Ganea, T., Hilton, P. J. and Peterson, F. P., On the homotopy-commutativity of loop-spaces and suspension. Topology 1 (1966) 133-141.Google Scholar
6. P. J. Hilton, , Homotopy theory and duality, Gordon and Breach (New York) 1963.Google Scholar