Pentagon equations, Voronoï tilings and pure braid groups invariant

2024/05/16 by Illia E. Rohozhkin, Rohozhkin, Illia E. · 2 citations
Mathematics · Physics and Astronomy · #57K10 #57K20 #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric Topology (math.GT) #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.10240

openalex publication_date 2024/05/16 · openalex created_date 2024/05/18 · openalex updated_date 2026/07/28

Abstract

In the present paper, we construct (2n-4)× (2n-4) matrices corresponding to the motion of points on standard round sphere from the point of view of Delaunay triangulations. We define homomorphism from spherical pure braids on n strands to the product of these matrices for n>5.

Cited by

• Tropical Ptolemy Transformations and Invariants of Braids
• Shear coordinates and braid invariants

Related

• Artin's braids, Braids for three space, and groups Γ_n⁴ and G_n^k
• Braid and knot invariants via triangulations and Ptolemy relations I
• Braids act on configurations of lines
• Presentations of braid groups of type A arising from (m+2)-angulations of regular polygons
• Braid groups are linear