All Tied Up: A First Look At Modern Yo-Yo and Knot Theory

TL;DR

This paper applies knot theory to classify and analyze string configurations in modern Yo-Yo play, bridging the gap between physical tricks and topological mathematics to enhance understanding and innovation.

Contribution

It introduces a systematic knot-theoretic framework for classifying Yo-Yo string mounts and relates them to topological moves, fostering collaboration between practitioners and mathematicians.

Findings

Classified Yo-Yo mounts using knot theory.

Identified correspondence between Yo-Yo maneuvers and Reidemeister moves.

Analyzed the effect of mounts on diagram writhe.

Abstract

Modern Yo-Yo play has developed into a sophisticated international subculture, featuring elite competition and intricate tricks. Despite this, no systematic knot-theoretic treatment has yet been applied to the numerous string configurations realised in contemporary Yo-Yo play. This paper takes initial steps in addressing this gap, recalling fundamental results from knot theory and embeddings to develop a methodology for classifying string arrangements, known as `mounts', in both beginner and advanced single Yo-Yo play. We classify a range of mounts according to the knots they form under appropriate post-processing procedures and identify Yo-Yo maneuvers that correspond to Reidemeister moves. Furthermore, we analyse the impact of certain mounts on the writhe of their diagrammatic projections and introduce operations to facilitate discussion of composite mounts. This work seeks to initiate a dialogue between Yo-Yo practitioners and knot theorists, fostering further advancements in high-level Yo-Yo play and enabling novel physical realisations of knots, links, braids, surgeries, and other topological transformations.