The Curtis–Wellington spectral sequence through cohomology

We study stable homotopy groups through unstable methods applied to their representing infinite loop space Q 0 S 0 , as pioneered by Curtis and Wellington.Using cohomology instead of homology, we find a width filtration whose subquotients are simple quotients of Dickson algebras, which thus gives a new filtration of stable homotopy groups.We make initial calculations and determine towers in the resulting width spectral sequence.We also make calculations related to the image of J, and prove that the J homomorphism induces a splitting of the indecomposables of the cohomology of Q 0 S 0 .