Pure virtual braids, resonance, and formality
arXiv:1602.04273 · doi:10.1007/s00209-016-1811-x
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.
31 pages; accepted for publication in Mathematische Zeitschrift