Cohomology of Hopf algebras and Massey products

The theory of the trigraded Buchstaber spectral sequence $\operatorname{Bss}$ for graded Hopf algebras is developed. It is shown that the differentials of $\operatorname{Bss}$ define an increasing exhaustive filtration as a new structure in the cohomology of Hopf algebras. This structure is described explicitly for a number of known Hopf algebras.
For the tensor algebra $T(s \operatorname{Ext}^{1,*}_{A}(\Bbbk,\Bbbk))$ of the suspension of the one-dimensional cohomology of a Hopf algebra $A$ over a field $\Bbbk$, the construction of partial multivalued operations $\operatorname{Bss}_p$, $p\geqslant 1$, is presented. This construction is used to describe the differentials in the spectral sequence $\operatorname{Bss}$ and the exhaustive filtration in $\operatorname{Ext}_{A}^{*,*}(\Bbbk,\Bbbk)$.
It is shown that the structure introduced is an effective tool for solving several well-known problems: (1) realising cohomology classes of Hopf algebras by Massey products; (2) interpreting differentials in $\operatorname{Bss}$ as Massey operations; (3) effective construction of a certain class of Massey products in the form of differentials in $\operatorname{Bss}$.
Bibliography: 74 titles.