Detection of a nontrivial product in the stable homotopy groups of spheres

Abstract

Let S be the sphere spectrum localized at an odd prime p and let A be the mod p Steenrod algebra. To determine the stable homotopy groups of spheres S is one of the central problems in homotopy theory. One of the main tools for investigating this problem is the Adams spectral sequence (ASS) E 2 D Ext A .Zp;Zp/) t sS , where the E 2 –term is the cohomology of A and the Adams differential is dr W E r !