A presentation for the planar pure braid group

Abstract

We describe the construction of a minimal presentation for the group of planar pure braids ${\overline{P}}_n$ on $n$ strands. The generators of this presentation are dual to the generators of the cohomology ring of ${\overline{P}}_n$ found by Y.Baryshnikov while the relations lie in the commutator subgroup of ${\overline{P}}_n$. We also construct an explicit (although non-minimal) presentation for the pure cactus group.

References in corpus (1)

• Structural aspects of twin and pure twin groups

Cited by in corpus (1)

• The planar pure braid group is a diagram group