Gottlieb Sets and Duality in Homotopy Theory
Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1042-1055

Voir la notice de l'article provenant de la source Cambridge University Press

Evaluation subgroups of the homotopy groups have been objects of extensive study recently by Gottlieb, Haslam, Jerrold Siegel, G. E. Lang (Jr), etc. In [8] one of the authors has introduced the notions of ‘cyclic' and ‘cocyclic’ maps and studied generalizations of evaluation subgroups and their duals in the set up of Eckmann-Hilton duality. This paper continues the study of these generalized Gottlieb and dual Gottlieb subsets. All the spaces, except the function spaces, will be arc connected locally compact CW-complexes with base point at a vertex. For any X, Y the set of base point preserving homotopy classes of maps of X to Y is denoted by [X, Y].
Halbhavi, I. G.; Varadarajan, K. Gottlieb Sets and Duality in Homotopy Theory. Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1042-1055. doi: 10.4153/CJM-1975-110-0
@article{10_4153_CJM_1975_110_0,
     author = {Halbhavi, I. G. and Varadarajan, K.},
     title = {Gottlieb {Sets} and {Duality} in {Homotopy} {Theory}},
     journal = {Canadian journal of mathematics},
     pages = {1042--1055},
     year = {1975},
     volume = {27},
     number = {5},
     doi = {10.4153/CJM-1975-110-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-110-0/}
}
TY  - JOUR
AU  - Halbhavi, I. G.
AU  - Varadarajan, K.
TI  - Gottlieb Sets and Duality in Homotopy Theory
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 1042
EP  - 1055
VL  - 27
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-110-0/
DO  - 10.4153/CJM-1975-110-0
ID  - 10_4153_CJM_1975_110_0
ER  - 
%0 Journal Article
%A Halbhavi, I. G.
%A Varadarajan, K.
%T Gottlieb Sets and Duality in Homotopy Theory
%J Canadian journal of mathematics
%D 1975
%P 1042-1055
%V 27
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-110-0/
%R 10.4153/CJM-1975-110-0
%F 10_4153_CJM_1975_110_0

[1] 1. Allaud, Guy, On the classification of fibre spaces, Math. Z. 92 (1966), 110–125. Google Scholar

[2] 2. Eckmann, B., Groupes d'homotopie et dualité, Bull. Soc. Math. France 86 (1958), 271–281. Google Scholar

[3] 3. Gottlieb, D. H., Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729–755. Google Scholar

[4] 4. Gottlieb, D. H., On fibre spaces and the evaluation map, Ann. of Math. 87 (1968), 42–45. Google Scholar

[5] 5. Hilton, P. J., Homotopy theory and duality (Gordon and Breach, New York, 1965). Google Scholar

[6] 6. Lang, G. E. (Jr), Evaluation subgroups and related topics, Ph.D. Thesis, Purdue University, 1970. Google Scholar

[7] 7. Spanier, E. H., Algebraic topology (McGraw Hill, New Yrork, 1966). Google Scholar

[8] 8. Varadarajan, K., Generalised Gottlieb groups, J. Indian Math. Soc. 83 (1969), 141–164. Google Scholar

[9] 9. Varadarajan, K., Groups for which Moore spaces M(ir, 1) exist, Ann. of Math. 84 (1966), 368–371 Google Scholar

Cité par Sources :