Mathematische Zeitschrift

, Volume 286, Issue 3–4, pp 1495–1524 | Cite as

Pure virtual braids, resonance, and formality



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.


Pure virtual braid groups Lower central series Chen ranks Alexander invariants Resonance varieties Holonomy Lie algebra 1-Formality Graded-formality Filtered-formality 

Mathematics Subject Classification

Primary 20F36 Secondary 16S37 20F14 20F40 20J05 55P62 57M07 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Department of Mathematics and StatisticsUniversity of NevadaRenoUSA

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