Classification of the stable homotopy types of stunted lens spaces for an odd prime (Q1358955)

For an odd prime \(p\), the complete classification of the stable homotopy types of stunted lens spaces mod \(p\) is obtained, following the method initiated at the prime 2 by Feder, Gitler, and Mahowald. The result is that for \(\delta,\epsilon\in\{0,1\}\), if \(L_{2n+\delta}^{2n+2l+\epsilon}\) and \(L_{2m+\delta} ^{2m+2l+\epsilon}\) are neither \(S\)-reducible nor \(S\)-coreducible, then they have the same stable homotopy type if and only if \(\nu_p(n-m)\geq[(l-1)/(p-1)]\). As was observed by the reviewer and Mahowald in the 2-primary case, two stunted lens spaces are stably equivalent if and only if they have isomorphic \(J\)-homology and \(J\)-cohomology.