A Braid Box

TL;DR

This paper presents an interactive art installation that visually demonstrates two definitions of braid groups and their actions, aiding understanding of complex topological concepts for learners.

Contribution

It introduces a novel interactive method to illustrate braid groups and their actions, making advanced topology accessible to non-specialists.

Findings

Successfully visualizes two definitions of braid groups.

Demonstrates all planar point motions within a T-shaped subspace.

Facilitates understanding of topological objects for students.

Abstract

We give a method for constructing an interactive art piece which illustrates two different definitions of the braid groups, along with their faithful action on the free group. The box also demonstrates how all motions of points in the plane can be realized by motions in a single T-shaped subspace of the plane. This helps students and those who are not specialists in algebraic topology to understand these important topological objects.