Unstable towers in the odd primary homotopy groups of spheres
Martin Bendersky · Transactions of the American Mathematical Society · 1985
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.