Stable homotopy types of stunted lens spaces mod 4 (Q2367022)

Let \(q=4\) or 8. In this paper, some necessary conditions and some sufficient conditions are obtained for stunted mod \(q\) lens spaces to have the same stable homotopy type. The conditions are very complicated to state. A list of cases in which the necessary and sufficient conditions agree is given. The sufficient conditions are obtained by recognizing the spaces as Thom complexes of \(J\)-equivalent bundles, while the necessary conditions are obtained by comparing the Atiyah-Adams \(J\)- groups of the spaces.