Artin's braids, Braids for three space, and groups Γ_n⁴ and G_n^k

2019/02/28 by V. O. Manturov, Manturov, V. O., Sera Kim +1
Mathematics · #57M25 #57M27 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1902.11238

openalex publication_date 2019/02/28 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We construct a group Γ_n⁴ corresponding to the motion of points in ℝ³ from the point of view of Delaunay triangulations. We study homomorphisms from pure braids on n strands to the product of copies of Γ_n⁴. We will also study the group of pure braids in ℝ³, which is described by a fundamental group of the restricted configuration space of ℝ³, and define the group homomorphism from the group of pure braids in ℝ³ to Γ_n⁴. In the end of this paper we give some comments about relations between the restricted configuration space of ℝ³ and triangulations of the 3-dimensional ball and Pachner moves.

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