The pure braid groups and their relatives

Alexander I. Suciu; He Wang

doi:10.1007/978-3-319-58971-8_15

The pure braid groups and their relatives

Group Theory 2017-12-12 v2 Geometric Topology

Authors: Alexander I. Suciu , He Wang

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Abstract

In this mostly survey paper, we investigate the resonance varieties, the lower central series ranks, and the Chen ranks, as well as the residual and formality properties of several families of braid-like groups: the pure braid groups $P_n$ , the welded pure braid groups $wP_n$ , the virtual pure braid groups $vP_n$ , as well as their `upper' variants, $wP_n^+$ and $vP_n^+$ . We also discuss several natural homomorphisms between these groups, and various ways to distinguish among the pure braid groups and their relatives.

Keywords

braid groups

Cite

@article{arxiv.1602.05291,
  title  = {The pure braid groups and their relatives},
  author = {Alexander I. Suciu and He Wang},
  journal= {arXiv preprint arXiv:1602.05291},
  year   = {2017}
}

Comments

24 pages; expanded version, to appear in the proceedings of the intensive research period on Perspectives in Lie theory (Pisa, 2015), Springer INdAM series

The pure braid groups and their relatives

Abstract

Keywords

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