Artin's braids, Braids for three space, and groups ${\Gamma }_n^4$ and $G_n^k$

V. O. Manturov, S. Kim

We construct a group ${\Gamma }_n^4$ corresponding to the motion of points in ${\mathbb{R}}^3$ from the point of view of Delaunay triangulations. We study homomorphisms from pure braid…