\(J\)-groups of suspensions of stunted lens spaces mod 8 (Q1324963)

Let \(L^ m_ 8\) denote the standard lens space \(S^{2n+ 1}/ \mathbb{Z}_ 8 \bmod 8\). In this paper the authors determine the structures: (1) the KO-groups \(\widetilde {\text{KO}} (S^ j (L^ m_ 8 / L^ n_ 8))\), \(m \geq \varphi (n,j)\); (2) the \(J\)-groups \(\widetilde{J}(S^ j (L^ m_ 8/L^ m_ 8))\), \(m\geq \psi(n,j)\), in which \(S\) is the suspension functor and \(\varphi (n,j)\) and \(\psi(n,j)\) are certain arithmetic functions of \(n\) and \(j\). The calculations are based on some results by Adams, Mahammed, Kobayashi, Sugawara and the authors.