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Multiplication on Spaces with Comultiplication*

Published online by Cambridge University Press:  20 November 2018

C.S. Hoo
C.S. Hoo*
Affiliation:
University of Alberta, Edmonton
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Let A be an H-space and K a space. It is well known that [K, A] is a loop. Suppose A has a comultiplication as well, that is, cat A < 2. Then we shall prove that [K, A] is a Moufang loop. This generalises a result of C. W. Norman who proved this for the case where A is the circle, the 3-sphere or the 7-sphere. It also improves the known result that [K, A] is a diassociative loop if A has a comultiplication as well, since Moufang loops are diassociative.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 499 - 505
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

*

This research was supported by NRC Grant A-3026.

References

1. Bruck, R.H., Contributions to the theory of loops. Trans. Amer. Math. Soc. 60 (1946) 245–354.Google Scholar
2. Bruck, R.H., A survey of binary systems. (Springer-Verlag, New York, 1966.)Google Scholar
3. Ganea, T., On some numerical homotopy invariants. Proc. Int. Congress of Mathematicians (1962) 467–472.Google Scholar
4. Ganea, T., Hilton, P.J. and Peterson, F. P., On the homotopycommutativity of loop-spaces and suspensions. Topology 1 (1962) 133–142.Google Scholar
5. Hilton, P.J., Homotopy theory and duality. (Gordon and Breach, New York, 1965.)Google Scholar
6. Hoo, C.S., A note on a theorem of Ganea, Hilton and Peterson. Proc. Amer. Math. Soc. 19 (1968) 909–911.Google Scholar
7. Hoo, C.S., On the suspension of an H-space. Duke Math. J. 36 (1969) 315–324.Google Scholar
8. Norman, C.W., Homotopy loops. Topology 2 (1963) 23–43.Google Scholar
9. O'Neill, R. C., On H-spaces that are CW-complexes, I. I11. J. Math. 8 (1964) 280–290.Google Scholar