Encoding and Topological Computation on Textiles

A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The first important problem is to encode all textile structures i...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Bright, Matt, Kurlin, Vitaliy
Format: Article
Language:English
Subjects:
Algorithms
Combinatorial analysis
Computation
Knot theory
Textiles
Topology
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The first important problem is to encode all textile structures in a simple combinatorial way. This paper extends the notion of the Gauss code in classical knot theory, providing a tool for topological computation on these structures. As a first application, we present a linear time algorithm for determining whether a code represents a textile in the physical sense. This algorithm, along with invariants of textile structures, allowed us for the first time to classify all oriented textile structures woven from a single component up to complexity five.
ISSN:2331-8422
DOI:10.48550/arxiv.2007.14871