Numerical computation of braid groups

TL;DR

This paper introduces a numerical algorithm for computing braid groups associated with curves, hyperplane arrangements, and polynomial systems, enabling the determination of their cross-locus and generators.

Contribution

The paper presents a novel numerical method for computing braid groups and their generators, advancing computational tools in algebraic topology.

Findings

Algorithm effectively computes braid groups for various geometric configurations.

Successfully determines cross-locus and generators of braid groups.

Provides a practical computational approach for algebraic topology problems.

Abstract

In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators of the braid group.