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On Evaluation Subgroups of Generalized Homotopy Groups

Published online by Cambridge University Press:  20 November 2018

K. L. Lim
K. L. Lim*
Affiliation:
Department of Economics And Statistics National University of Singapore Kent Ridge, Singapore 0511
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Abstract

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G(A, X) consists of all homotopy classes of cyclic maps from a space A to another space X. If A is an H-cogroup, then G(A, X) is a group. G(A, X) preserves products in the second variable and is a contravariant functor of A from the full subcategory of H-cogroups and maps into the category of abelian groups and homomorphisms. If X is an H-cogroup, then G(X, X) is a ring.

Keywords

55E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 78 - 86
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Arkowitz, M., The generalized Whitehead Product, Pacific J. Math. 12 (1962), 7-23.Google Scholar
2. Arkowitz, M. and Curjel, C. R., On maps of H-spaces, Topology 6 (1967), 137-148.Google Scholar
3. Ganea, T., Induced fibrations and cofibrations, Trans. Amer. Math. Soc. 127 (1967), 442-459.Google Scholar
4. Gottlieb, D. H., A certain subgroup of the fundamental group, Amer. J. Maths. 87 (1965), 840-856.Google Scholar
5. Gottlieb, D. H., Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756.Google Scholar
6. Hoo, C. S., On the suspension of an H-space, Duke Maths. J. 36 (1969), 315-324.Google Scholar
7. Hoo, C. S., Cyclic maps from suspensions to suspensions, Can. J. Math. 24 (1972), 789-791.Google Scholar
8. Hu, S. T., Homotopy theory (Academic Press, New York, 1959).Google Scholar
9. Lim, K. L., On cyclic maps, The Journal of the Australian Math. Soc. (Series A) 32 (1982), 349-357.Google Scholar
10. Porter, G. J., Spaces with vanishing Whitehead products, Quart. J. Math., Oxford Ser. (2) 16 (1965), 77-84.Google Scholar
11. Siegel, J., G-spaces, H-spaces and W-spaces, Pacific J. Math. 31 (1969), 109-214.Google Scholar
12. Varadarajan, K., Generalized Gottlieb groups, J. Ind. Math. Soc. 33 (1969), 141-164.Google Scholar