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The Fibre of the Double Suspension is an H-Space

Published online by Cambridge University Press:  20 November 2018

Paul Selick
Paul Selick*
Affiliation:
University of TorontoScarborough Campus Scarborough, Ontario MIC 1A4
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Abstract

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In this paper we show that the homotopy-theoretic fibre of the double suspension map E2:S2n-1 → Ω2S2n+1 is an H-space.

Keywords

55P45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 1 , 01 March 1985 , pp. 124 - 128
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Adams, J.F., On the non-existence of elements of Hopf invariant one, Ann. of Math., 72 (1960), pp. 20–104.Google Scholar
2. Campbell, H.E.A., Peterson, F.P., and Selick, P.S., Self-maps of loop spaces, I, to appear in Trans. Amer. Math. Soc.Google Scholar
3. Campbell, H.E.A., Cohen, F.R., Peterson, F.P., and Selick, P.S., Self-maps of loop spaces, II (in preparation).Google Scholar
4. Cohen, F.R., Lada, T.J., and May, J.P., The Homology of Iterated Loop Spaces, Lecture Notes in Math., 533 Springer-Verlag (1976).Google Scholar
5. Cohen, F.R. and Mahowald, M.E., A remark on the self-maps of Ω 2 S 2n+1 Indiana Univ. Math. J. 30 (1981), pp. 583–588.Google Scholar
6. Cohen, F.R., Moore, J.C., and Neisendorfer, J.A., Exponents in homotopy theory, to appear in Proc. John Moore Conf. on Alg. Topology and K-Theory, Annals of Math Studies.Google Scholar
7. James, I., The suspension triad of a sphere, Ann. of Math., 63 (1956), pp. 407—429.Google Scholar
8. Selick, P.S., A reformulation of the Arf invariant one modp problem and applications to atomic spaces, Pac. J. of Math., 108 (1983), pp. 431–450.Google Scholar
9. Sugawara, T., On a condition that a space is an H-space, Math. J. Okayama Univ., 6 (1957), pp. 109–129.Google Scholar
10. Toda, H., Composition Methods in Homotopy Groups of Spheres, Ann. of Math Studies, 49 (1962).Google Scholar