Homology, lower central series, and hyperplane arrangements

Abstract

We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our 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 an application to hyperplane arrangements, whereby we show that all the nilpotent quotients of a decomposable arrangement group are combinatorially determined.

arXiv comment34 pages; accepted for publication in the European Journal of Mathematics

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Cited by in corpus (2)

• Differential graded algebras, Steenrod cup-one products, binomial operations, and Massey products
• Milnor fibrations of arrangements with trivial algebraic monodromy