Higher structure in the unstable Adams spectral sequence

TL;DR

This paper introduces a new construction of the unstable Adams spectral sequence for spaces, linking differentials and filtrations to higher cohomology operations, enhancing understanding of its structure.

Contribution

It presents a novel variant construction of the unstable Adams spectral sequence using free simplicial resolutions, clarifying its differentials and filtration through higher cohomology operations.

Findings

New construction of the spectral sequence

Explicit description of differentials and filtration

Connection to higher cohomology operations

Abstract

We describe a variant construction of the unstable Adams spectral the sequence for a space $Y$, associated to any free simplicial resolution of $H^*(Y;R)$ 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.