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On the Homotopy-Commutativity of Loop-Spaces and 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 X be a space. We are interested in the homotopy-commutativity of the loop-space ΩX and the suspension ΣX, that is, in the question whether or not nil X ≦ 1, conil X ≦ 1, respectively. Let c: ΩX× ΩX ⟶ ΩX, c': ΣX ⟶ ΣX V ΣX be the commutator and co-commutator maps, respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1531 - 1536
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Berstein, I. and Ganea, G., Homotopical nilpotency, Illinois J. Math. 5 (1961), 99–130.Google Scholar
2. Berstein, I. and Hilton, P. J., On suspensions and comultiplications, Topology 2 (1963), 73–82.Google Scholar
3. Ganea, T., Hilton, P. J., and Peterson, F. P., On the homotopy-commutativity of loop-spaces and suspensions, Topology 1 (1962), 133–141.Google Scholar
4. Hilton, P. J., Homotopy theory and duality (Gordon and Breach, New York, 1965).Google Scholar