Cat\'egorification des coefficients de la matrice de la repr\'esentation de Burau

TL;DR

This paper introduces a geometric categorification of the coefficients in the Burau representation matrix, demonstrating its effectiveness in identifying trivial braids.

Contribution

It provides a novel geometrical approach to categorify the Burau representation coefficients, proving its faithfulness in detecting trivial braids.

Findings

Categorification using elementary geometrical methods.

Faithfulness of the categorification in detecting trivial braids.

Enhanced understanding of the Burau representation structure.

Abstract

We categorify the coefficients of the Burau representation matrix using elementary geometrical methods. We show the faithfulness of this categorification in the sense that it detects the trivial braid.