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A group of automorphisms of the homotopy groups
- Source :
- Nagoya Math. J. 2 (1951), 73-82
- Publication Year :
- 1951
- Publisher :
- Duke University Press, 1951.
-
Abstract
- 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
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Nagoya Math. J. 2 (1951), 73-82
- Accession number :
- edsair.doi.dedup.....40d1f80b41f0a648eaf451d4e9aebb98