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A Group of Automorphisms of the Homotopy Groups

Published online by Cambridge University Press:  22 January 2016

Hiroshi Uehara
Hiroshi Uehara*
Affiliation:
Mathematical Institute, Nagoya University
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It is well known that the fundamental group π1(X) of an arcwise connected topological space X operates on the n-th homotopy group πn(X) of X as a group of automorphisms. In this paper I intend to construct geometrically a group 𝒰(X) of automorphisms of πn(X), for every integer n ≥ 1, which includes a normal subgroup isomorphic to π1(X) so that the factor group of 𝒰(X) by π1(X) is completely determined by some invariant Σ(X) of the space X. The complete analysis of the operation of the group on πn(X) is given in §3, §4, and §5,

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 2 , February 1951 , pp. 73 - 82
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1951

References

[1] Eilenberg, S., On the relation between the fundamental group of a space and higher homotopy groups, Fundamenta Math, 32 (1939).Google Scholar
[2] Hu, S. T., On the Whitehead Group of automorphisms of the relative homotopy groups, Portugaliae Math. 7 (1948).Google Scholar