The cat's cradle, stirring, and topological complexity

TL;DR

This paper explores how elementary topology constrains the possible mappings of loops and surfaces, with applications to physical systems like fluid stirring and the game of cat's cradle, highlighting the role of topological complexity.

Contribution

It introduces a topological framework for understanding constraints on loop entanglements and surface mappings in physical systems, connecting topology with fluid dynamics and recreational puzzles.

Findings

Topological constraints limit loop entanglements in physical systems

Elementary topology informs possible surface mappings in fluid stirring

The study links topological complexity to physical phenomena

Abstract

There are several physical situations in which the `tangling' of a loop is relevant: the game of cat's cradle is a simple example, but a more important application involves the stirring of a fluid by rods. Here we discuss how elementary topology constrains the types of mappings that can occur on a surface, for example when the surface is the domain of a two-dimensional fluid.