Higher structure in the unstable Adams spectral sequence

Abstract

We describe a variant construction of the unstable Adams spectral the sequence for a space $Y$, associated to any free simplicial resolution of $H^{\ast }(Y;R)$ for $R={\mathbb{F}}_p$ or $\mathbb{Q}$. We use this construction to describe the differentials and filtration in the spectral sequence in terms of appropriate systems of higher cohomology operations.