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Pentagon equations, Delaunay triangulations and pure braid group invariant

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arxiv 2405.10240 v2 pith:UYU5N5VV submitted 2024-05-16 math.AT math.GT

Illia E. Rohozhkin This is my paper · ORCID
classification math.ATmath.GT
keywords groupbraiddelaunaypuretriangulationsconstructcorrespondingdefine
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abstract

We construct $(2n+1)\times (2n+1)$ matrices corresponding to a motion of points on the plane from the point of view of Delaunay triangulations. We define a homomorphism from the pure braid group on ($n+3$) strands to the general linear group $\text{GL}_{2n+1}(\mathbb{Q})$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Shear coordinates and braid invariants

    math.GT 2025-05 conditional novelty 5.0 of 10

    The paper constructs a braid invariant from shear-coordinate transformations applied to the edges of Delaunay triangulations.

  2. Octagon and tropical octagon yield braid invariants

    math.GT 2024-11 reject novelty 5.0 of 10

    Braids in the projective plane act on labels of a dual graph via the Desargues flip, and isotopic braids produce identical label transformations.

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