# Braid and knot invariants via triangulations and Ptolemy relations I

## TL;DR

This paper introduces a novel method for constructing invariants of braids, knots, and links by analyzing point dynamics in the plane and utilizing Ptolemy relations, bridging geometric and algebraic approaches.

## Contribution

It presents a new framework combining geometric dynamics and Ptolemy relations to define invariants for braids, knots, and links, advancing topological invariant theory.

## Key findings

- New invariants for braids, knots, and links derived
- Application of Ptolemy relations in topological invariants
- Potential connections to quantum topology and geometric structures

## Abstract

In this paper, we construct invariants of braids, knots and links by studying dynamics of points in $\R^{2}$ and applying the Ptolemy relation $ac+bd=xy$.

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Source: https://tomesphere.com/paper/1812.08436