common way of finding large-scale phenomena in the p-component of the stable homotopy groups of spheres requires finite CW-complexes in the stable category which admit vn -self-maps in the sense of Devinatz, Hopkins and Smith. Furthermore, it is desirable to find those CW-complexes which admit vn-self-maps whose periodicities are small. Finding these often requires difficult computations in homological algebra.;In joint work with Bhattacharya and Mahowald, we consider the case... |