Return to Revisions

Use Theorem 8.9 from Whitheads Elements of Homotopy Theory on page 537. Take $k=2$, $\beta=\iota_4$ and $\alpha\in\pi_8S^4$. Use $[\iota_4,\iota_4]=\Sigma\nu'-2\nu_4$, $h_0(\nu_4\circ\eta_7)=h_0(\nu)\circ\eta_8=\iota_7\circ\eta_8=\eta_8$ and $h_0(\Sigma\nu'\circ\eta_7)=h_0(\Sigma(\nu\circ\eta_6))=0$. The triple product disappears and you are left with the David Frank's answer.