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H-Semidirect Products

Published online by Cambridge University Press:  20 November 2018

Georg Peschke
Georg Peschke*
Affiliation:
University of Calgary Calgary, Alberta, CanadaT2N 1N4
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Abstract

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The concept of H-semidirect product structure on a grouplike space is introduced. It is shown that the loop space ΩX of any based CW-complex X is the H-semidirect product of the identity path-component of ΩX with π1,X. The set of free homotopy classes of maps into a Hsemidirect product inherits the structure of a semidirect product. This leads to new results concerning the nilpotency of homotopy classes of maps into a group-like space.

Keywords

55D3555D4555E0555E35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 402 - 411
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Hilton, P.J., Nilpotent actions on nilpotent groups, Algebra and Logic; Springer Lecture Notes 450 (1975), pp. 174–197.Google Scholar
2. Milnor, J., On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959), pp. 272–280.Google Scholar
3. Roitberg, J., Note on nilpotent spaces and localization, Math. Z. 137 (1974), pp. 67–74.Google Scholar
4. Scheerer, H., Bemerkungen ueher Gruppen von Homotopieklassen, Archiv. Math. 28 (1977), pp. 301–307.Google Scholar
5. Varadarajan, K., Nilpotent actions and nilpotent spaces, unpublished (1976).Google Scholar
6. Whitehead, G.W., On mappings into group-like spaces, Comm. Math. Helv. 28 (1954), 320-328.Google Scholar
7. Whitehead, G.W., Elements of Homotopy Theory, Springer Verlag, New York (1978).Google Scholar
8. Arkowitz, M. and Curjel, C.R., On maps of'H-spaces, Topology 6 (1967), pp. 137–148.Google Scholar
9. Kahn, D.W., A note on H-equivalences, Pac. J. Math. 42 (1972), pp. 77–80.Google Scholar
10. Roitberg, J., Residually finite, Hopfian and Co-Hopfian Spaces, Contemporary Mathematics, AMSConference on Algebraic Topology in Honor of Peter Hilton 37 (1985), pp. 131–144.Google Scholar