Digraphs, pro-$p$ groups and Massey products in Galois cohomology

Abstract

Let $p$ be a prime. We characterize the oriented right-angled Artin pro-$p$ groups whose ${\mathbb{F}}_p$-cohomology algebra yields no essential $n$-fold Massey products for every $n>2$, in terms of the associated digraph. Moreover, we show that the ${\mathbb{F}}_p$-cohomology algebra of such oriented right-angled Artin pro-$p$ groups is isomorphic to the exterior Stanley-Reisner ${\mathbb{F}}_p$-algebra associated to the same digraph. This work also aims at providing a concrete and group-theoretic introduction to the study of Massey products in Galois cohomology for non-specialists, especially graduate students working in profinite group theory.

In this version we use the notion of "digraph" instead of the notion of "oriented graph" previously (and uncorrectly) used, and adapt the content suitably