Unstable towers in the odd primary homotopy groups of spheres

Bendersky, Martin

doi:10.1090/S0002-9947-1985-0768724-0

Unstable towers in the odd primary homotopy groups of spheres
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Trans. Amer. Math. Soc. 287 (1985), 529-542 Request permission

Abstract:

The unstable elements in filtration $2$ of the unstable Novikov spectral sequence are computed. These elements are shown to survive to elements in the homotopy groups of spheres which are related to $\operatorname {Im} J$. The computation is applied to determine the Hopf invariants of compositions of $\operatorname {Im} J$ and the exponent of certain sphere bundles over spheres.

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Unstable families related to the image of