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arXiv · 1602.04273

Pure virtual braids, resonance, and formality

Alexander I. Suciu·He Wang
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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.

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Alexander I. Suciu, He Wang. 2016-10-13. Pure virtual braids, resonance, and formality. https://doi.org/10.1007/s00209-016-1811-x

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