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Artin’s braids, braids for three space, and groups $Γ_{n}^{4}$ and $G_{n}^{k}$

Department of Fundamental Sciences, Bauman Moscow State Technical University, 2/18, Rubtsovskaya nab., 105005, Moscow, Russia

E-mail Address: ksj19891120@gmail.com

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V. O. Manturov

Department of Fundamental Sciences, Bauman Moscow State Technical University, 2/18, Rubtsovskaya nab., 105005, Moscow, Russia

Novosibirsk State University, Pirogova 1, 630090, Novosibirsk, Russia

E-mail Address: vomanturov@yandex.ru

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https://doi.org/10.1142/S0218216519500639Cited by:2 (Source: Crossref)

Abstract

We construct a group $Γ_{n}^{4}$ corresponding to the motion of points in $ℝ^{3}$ from the point of view of Delaunay triangulations. We study homomorphisms from pure braids on $n$ strands to the product of copies of $Γ_{n}^{4}$ . We will also study the group of pure braids in $ℝ^{3}$ , which is described by a fundamental group of the restricted configuration space of $ℝ^{3}$ , and define the group homomorphism from the group of pure braids in $ℝ^{3}$ to $Γ_{n}^{4}$ . At the end of this paper, we give some comments about relations between the restricted configuration space of $ℝ^{3}$ and triangulations of the 3-dimensional ball and Pachner moves.

Keywords:

AMSC: 57M25, 57M27

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