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Homology, lower central series, and hyperplane arrangements

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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 Grigory 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.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Richard D. Porter & Alexander I. Suciu

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  1. Richard D. Porter
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  2. Alexander I. Suciu
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Correspondence to Richard D. Porter.

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To the memory of Ştefan Papadima, 1953–2018

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A.I. Suciu partially supported by the Simons Foundation Collaboration Grant for Mathematicians # 354156.

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Porter, R.D., Suciu, A.I. Homology, lower central series, and hyperplane arrangements. European Journal of Mathematics 6, 1039–1072 (2020). https://doi.org/10.1007/s40879-019-00392-x

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