On Relations in the Cohomology of Hopf Algebras

In 1970, V. M. Buchstaber introduced a spectral sequence for computing the second term of the Adams–Novikov spectral sequence for the stable homotopy groups of spheres. In a recent work by V. M. Buchstaber and the author (Russian Mathematical Surveys, 2024), a theory of an analogous trigraded spectral sequence was developed for general Hopf algebras over a field. Using the cohomology of Steenrod algebras as an example, we will show how the differentials of this spectral sequence can be used to describe relations in the cohomology of Hopf algebras.