Pure virtual braids, resonance, and formality

Abstract

We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer to the 1-formality question for this class of groups. In the process, we explore various connections between the Alexander-type invariants of a finitely generated group and several of the graded Lie algebras associated to it, and discuss possible extensions of the resonance-Chen ranks formula in this context.

arXiv comment31 pages; accepted for publication in Mathematische Zeitschrift

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Cited by in corpus (7)

• Formality properties of finitely generated groups and Lie algebras
• The pure braid groups and their relatives
• Cup products, lower central series, and holonomy Lie algebras
• Chen ranks and resonance varieties of the upper McCool groups
• Poincaré duality and resonance varieties
• Cohomology, Bocksteins, and resonance varieties in characteristic 2
• On the topology of the Milnor fibration of a hyperplane arrangement