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- Title
Generalizations of Fox Homotopy Groups, Whitehead Products, and Gottlieb Groups.
- Authors
Golasiński, M.; Gonçalves, D.; Wong, P.
- Abstract
In this paper, we redefine the Fox torus homotopy groups and give a proof of the split exact sequence of these groups. Evaluation subgroups are defined and are related to the classical Gottlieb subgroups. With our constructions, we recover the Abe groups and prove some results of Gottlieb for the evaluation subgroups of Fox homotopy groups. We further generalize Fox groups and define a group τ = [Σ( V× W⋃ *), X] in which the generalized Whitehead product of Arkowitz is again a commutator. Finally, we show that the generalized Gottlieb group lies in the center of τ, thereby improving a result of Varadarajan.
- Subjects
HOMOTOPY groups; GROUP theory; ALGEBRA; EQUATIONS; MATHEMATICAL analysis; MATHEMATICS
- Publication
Ukrainian Mathematical Journal, 2005, Vol 57, Issue 3, p382
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-005-0197-4