Planar pure braids on six strands

Abstract

The group of planar (or flat) pure braids on $n$ strands, also known as the pure twin group, is the fundamental group of the configuration space $F_{n,3}(\mathbb{R})$ of $n$ labelled points in $\mathbb{R}$ no three of which coincide. The planar pure braid groups on 3, 4 and 5 strands are free. In this note we describe the planar pure braid group on 6 strands: it is a free product of the free group on 71 generators and 20 copies of the free abelian group of rank two.

References in corpus (1)

• Structural aspects of twin and pure twin groups

Cited by in corpus (10)

• Topological Exchange Statistics in One Dimension
• Structure and automorphisms of pure virtual twin groups
• Conjugacy classes and automorphisms of twin groups
• Some remarks on twin groups
• Automorphisms of odd Coxeter groups
• Congruence subgroups and crystallographic quotients of small Coxeter groups
• Topologically Nontrivial Three-Body Contact Interaction in One Dimension
• Virtual planar braid groups and permutations
• Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups
• Flat braid groups, right-angled Artin groups, and commensurability