Dualization of the Hopf algebra of secondary cohomology operations and the Adams spectral sequence

TL;DR

This paper develops explicit formulas for computing the E_3-term of the Adams spectral sequence by dualizing the algebra of secondary cohomology operations, extending the Milnor dual of the Steenrod algebra.

Contribution

It introduces a dualization approach for secondary cohomology operations, providing new explicit computational tools for the Adams spectral sequence.

Findings

Derived explicit formulas for the E_3-term

Extended the Milnor dual of the Steenrod algebra

Enhanced computational methods for stable homotopy groups

Abstract

We describe the dualization of the algebra of secondary cohomology operations in terms of generators extending the Milnor dual of the Steenrod algebra. In this way we obtain explicit formulae for the computation of the E_3-term of the Adams spectral sequence converging to the stable homotopy groups of spheres.