The pure cactus group is residually nilpotent

Abstract

We show that the pure cactus group ${\Gamma }_{n+1}$ is residually nilpotent and exhibit a surjective homomorphism ${\Gamma }_{n+1}\to (\mathbb{Z}/2\mathbb{Z}{)}^{2^n-n(n+1)/2-1}$ whose kernel is residually torsion-free nilpotent.