Pure virtual braids, resonance, and formality
Group Theory
2017-07-18 v2 Geometric Topology
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
Cite
@article{arxiv.1602.04273,
title = {Pure virtual braids, resonance, and formality},
author = {Alexander I. Suciu and He Wang},
journal= {arXiv preprint arXiv:1602.04273},
year = {2017}
}
Comments
31 pages; accepted for publication in Mathematische Zeitschrift