Mathematische Zeitschrift

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

Pure virtual braids, resonance, and formality

Article

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.

Keywords

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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