Title: The Curtis-Wellington Spectral Sequence Through Cohomology
Abstract: In this talk, we will discuss an unstable approach to studying stable homotopy groups as pioneered by Curtis and Wellington. Using the Barratt-Priddy-Quillen theorem, we can identify the (co)homology of BS∞ with the (co)homology of the base point component of the loop space which represents stable homotopy. Using cohomology instead of homology to exploit the nice Hopf ring presentation of Giusti, Salvatore, and Sinha for the cohomology of symmetric groups, we find a width filtration. The subquotients of this filtration are simple quotients of Dickson algebras, which thus give a new filtration of stable homotopy. We will discuss 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 Q0S0.