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The fibre of the iterated Freudenthal suspension. (English) Zbl 0793.55006
A classical construction in Algebraic Topology is the iterated Freudenthal suspension map which induces the suspension homomorphism on homotopy groups. In this paper, we give combinatorially defined constructions for the homotopy theoretic fibre of the iterated loops of the iterated Freudenthal suspension map. We further prove that these fibres admit stable decompositions. As an application, we obtain in the case of spheres certain cofibre sequences when localized at a single prime. In the case of the single suspension and at the prime 2, it reduces to a classical cofibre sequence involving Brown-Gitler spectra.
Reviewer: S.Wong (Rochester)
55P40 Suspensions
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