The \(E_2\) term of the spectral sequence of unstable homotopy groups of topological spaces (Q1966264)

The inspiration for the present paper is [\textit{W. S. Massey} and \textit{F. P. Peterson}, The mod 2 cohomology structure of certain fibre spaces, Mem. Am. Math. Soc. 74 (1967; Zbl 0168.44002)]. The goal is to analyze an \(E_2\) term for an unstable Adams spectral sequence. With \(K\) the dual of the Steenrod algebra (the Milnor algebra) and \(L\) an unstable co-module, the author examines a co-bar construction. The main technical innovation is to work with bigraded differential algebras and modules. For \(K\) the first grading is always zero and the second is the standard one. The co-bar functor on \(K\) yields a monade in the category at hand, whose homology acquires an \(A_\infty\)-structure. This permits the author to give a description -- in terms of generators and relations -- of the \(E_2\) terms for spheres. No specific calculations of homotopy groups are included here.