On Toda’s fibrations. (English) Zbl 0572.55013
Let p be an odd prime and \(S^{2n-1}\to \Omega S^{2n}_{(p- 1)}\to^{H'}\Omega S^{2np-1}\) be the p-localized fibration introduced by H. Toda [J. Inst. Polytechn., Osaka City Univ., Ser. A 7, 103- 145 (1956; Zbl 0073.183)]. The author gives another definition of H’, which is natural, is an H-map and behaves well with respect to the Dyer- Lashof map \(B\Sigma_ p\to \Omega (S^ 0)\).
Reviewer: Y.Furukawa
MSC:
| 55R05 | Fiber spaces in algebraic topology |
| 55Q25 | Hopf invariants |
| 55P35 | Loop spaces |
| 55P60 | Localization and completion in homotopy theory |
Citations:
Zbl 0073.183References:
| [1] | Toda, J. Inst. Polytech. Osaka City Univ. 7 pp 103– (1956) |
| [2] | DOI: 10.1007/BF02564562 · Zbl 0052.19501 · doi:10.1007/BF02564562 |
| [3] | DOI: 10.1112/plms/s3-26.3.497 · Zbl 0263.55012 · doi:10.1112/plms/s3-26.3.497 |
| [4] | Gray, J. Math. Proc. Cambridge Philos. Soc. 96 pp 95– (1984) |
| [5] | DOI: 10.1007/BF01393932 · Zbl 0444.55011 · doi:10.1007/BF01393932 |
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