Square rings associated to elements in homotopy groups of spheres (Q2734858)

Suppose that \(\Sigma X\) is an \((m-1)\)-connected space of dimension \(< 3m -3\) with \(M \geq 2\). Let \(Q_{e}\) denote \([\Sigma X, \Sigma X]\), and \(Q_{ee}\) denote \([\Sigma X, \Sigma X \wedge X]\) then \(Q = (Q_{e} @ >\alpha>>{\overline{H}}{\rightarrow} Q_{ee} @ >\alpha>>{\overline P}{\rightarrow} Q_{e})\), where \(\overline H\) is the Hopf invariant and \(\overline P\) is induced by the Whitehead product, determines a square ring. The authors calculate this square ring for the case where \(\Sigma X = \Sigma C_{\alpha}\) with \(\alpha \in \pi_{n-2}(S^{m-1})\) and \(n < 3m -3\). The answer is given in terms of primary homotopy operations on spheres.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00050].