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On the Group Structure in Homotopy Groups

Published online by Cambridge University Press:  22 January 2016

Masatake Kuranishi
Masatake Kuranishi*
Affiliation:
Mathematical Institute, Nagoya University
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Usually the group structure in a homotopy group is defined directly and explicitly. But the algebraic approach to the topology, now common, seems to raise the following question : is that the only group sturcture which is natural from the algebraic topological point of view? On the other hand, several algebraists have begun to feel a necessity to construct a “homotopy or cohomotopy theory of groups,” and it may be allowed to say that one of the first steps to the problem is the axiomatization of homotopy groups. Our first question is of course a special case of the latter problem.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 7 , June 1954 , pp. 133 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1954

References

[ 1 ] Iwahori, N. and Hattori, A., On associative compositions in finite nilpotent groups, Nagoya Math. J., this number.Google Scholar
[ 2 ] Morimoto, A., A lemma on a free group, Nagoya Math. J., this number,Google Scholar