A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods

TLDR

Textile structures can be viewed as knots or links represented on a torus, and the basics of knot theory are briefly introduced. The paper proposes a systematic approach to describe and classify textile structures using topological principles. The authors develop a method that enumerates textile structures and computes topological invariants of doubly‑periodic structures. This approach allows modern knot theory methods to be applied to textile topology.

Abstract

This paper proposes a new systematic approach for the description and classification of textile structures based on topological principles. It is shown that textile structures can be considered as a specific case of knots or links and can be represented by diagrams on a torus. This enables modern methods of knot theory to be applied to the study of the topology of textiles. The basics of knot theory are briefly introduced. Some specific matters relating to the application of these methods to textiles are discussed, including enumeration of textile structures and topological invariants of doubly-periodic structures.