Shear coordinates and braid invariants
Vassily Olegovich Manturov
TL;DR
This paper introduces a novel approach using shear coordinates in hyperbolic geometry to derive invariants of braids, with an additional tropical analogue, advancing the understanding of braid invariants.
Contribution
It presents a new method leveraging shear coordinates for braid invariants and introduces a tropical analogue, bridging hyperbolic geometry and braid theory.
Findings
Shear coordinates can be used to define braid invariants.
A tropical analogue of the shear coordinate method is developed.
The approach provides new tools for studying braid invariants.
Abstract
We present a way of using shear coordinates in hyperbolic geometry to get invariants of braids. This method also has a tropical analogue.
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Taxonomy
TopicsGeometric and Algebraic Topology · Polynomial and algebraic computation · Homotopy and Cohomology in Algebraic Topology