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On cyclic maps

Published online by Cambridge University Press:  09 April 2009

K. L. Lim
K. L. Lim
Affiliation:
Department of Economics and Statistics, National University of Singapore, Singapore
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Abstract

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The definition of cyclic maps is recalled and their existence discussed. Among other things, it is shown that cyclicity of maps is closed under product and that if f is cyclic then Ωf is central.Some results of Gottlieb (1972) on homology are applied to investigate the relationship between cyclicity of maps and maps of finite order.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 349 - 357
Copyright
Copyright © Australian Mathematical Society 1982

References

Arkowitz, M. and Curjel, C. R. (1964), Groups of homotopy classes (Lecture Notes in Mathematics, Vol. 4, Springer-Verlag).CrossRefGoogle Scholar
Arkowitz, M. and Curjel, C. R. (1967), ‘On maps of H-spaces’, Topology 6, 137–148.CrossRefGoogle Scholar
Ganea, T. (1967), ‘Induced fibrations and cofibrations’, Trans. Amer. Math. Soc. 127, 442–459.CrossRefGoogle Scholar
Ganea, T. (1968), ‘Cyclic homotopies’, Illinois J. Math. 12, 1–4.CrossRefGoogle Scholar
Gottlieb, D. H. (1965), ‘A certain subgroup of the fundamental group’, Amer. J. Math. 87, 840–856.CrossRefGoogle Scholar
Gottlieb, D. H. (1969), ‘Evaluation subgroups of homotopy groups’, Amer. J. Math. 91, 729–756.CrossRefGoogle Scholar
Gottlieb, D. H. (1972), ‘The evaluation map and homology’, Michigan Math. J. 19, 289–297.CrossRefGoogle Scholar
Hoo, C. S. (1972), ‘Cyclic maps from suspensions to suspensions’, Canad. J. Math. 24, 789–791.CrossRefGoogle Scholar
Hu, S. T. (1959), Homotopy theory (Academic Press, New York).Google Scholar
Lang, G. E. Jr (1970), Evaluation subgroups and related topics (Ph. D. dissertation, Purdue Univ.).Google Scholar
Varadarajan, K. (1969), ‘Generalized Gottlieb groups’, J. Indian Math. Soc. 33, 141–164.Google Scholar