Holonomy Lie algebras, lifting theorems, Massey products, and hyperplane arrangements

In joint work with Alex Suciu, we explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. The main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain commuting diagrams. This recasts a result of G. Rybnikov in a more general framework and leads to a generalization of Massey triple products and an application to hyperplane arrangements, whereby we show that all the nilpotent quotients of a decomposable hyperplane arrangement are combinatorially determined.