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On Toda's fibrations

Published online by Cambridge University Press:  24 October 2008

Brayton Gray
Brayton Gray
Affiliation:
Department of Mathematics, University of Illinois at Chicago
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Extract

In 1956 Toda [5] introduced two fibrations localized at p > 2:

where is a subcomplex of the James construction . The construction of H′ was somewhat difficult and was discussed by Moore (see [3]). Moore's definition however is not natural (in the sense of Theorem 1 (b) below). It is our purpose to give another definition, closer to Toda's original definition, which is natural, is an H map* and behaves well with respect to the Dyer-Lashof map λ: BΣp → Q(So). We use this to settle an unanswered question in [2].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 289 - 298
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Gray, B.. On the homotopy groups of mapping cones. Proc. London Math. Soc. (3) 26 (1973), 497–520.CrossRefGoogle Scholar
[2]Gray, B.. Unstable families related to the image of J. Math. Proc. Cambridge Philos. Soc. 96 (1984), 95–113.CrossRefGoogle Scholar
[3]Selick, P.. A spectral sequence concerning the double suspension. Invent. Math. 64 (1981), 15–24.CrossRefGoogle Scholar
[4]Serre, J. P.. Cohomologie modulo 2 des complexes d'eilenberg-MacLane. Comment. Math. Helv. 27 (1953), 198–232.CrossRefGoogle Scholar
[5]Toda, H.. On the double suspension E2. J. Inst. Polytech. Osaka City Univ. 7 (1956) 103–145.Google Scholar