The Pure Braid Groups and Their Relatives

2016/02/29 by Alexander I. Suciu, He Wang
Mathematics · #Advanced Algebra and Geometry #Braid #Braid group #Combinatorics #Formality #Geometric and Algebraic Topology #Group (periodic table) #History #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Linguistics #Mathematics #Philosophy #Physics #math.GR #math.GT #msc:16S37 #msc:20F14 #msc:20F36 #msc:20F40 #msc:20J05 #msc:55P62 #msc:57M07

paper · pdf · doi:10.1007/978-3-319-58971-8_15

published as Perspectives in Lie theory, 403-426, Springer INdAM series, vol. 19, Springer, Cham, 2017 · 24 pages; expanded version, to appear in the proceedings of the intensive research period on Perspectives in Lie theory (Pisa, 2015), Springer INdAM series

arxiv created 2016/05/29 · openalex publication_date 2017/01/01 · arxiv updated 2017/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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