A Topological Study of Textile Structures. Part II: Topological Invariants in Application to Textile Structures

被引：20

作者：

Grishanov, S. ^{[1
]}

Meshkov, V. ^{[2
]}

Omelchenko, A. ^{[2
]}

机构：

[1] De Montfort Univ, TEAM Res Grp, Leicester LE1 9BH, Leics, England

[2] St Petersburg State Polytech Univ, St Petersburg, Russia

来源：

TEXTILE RESEARCH JOURNAL | 2009年 / 79卷 / 09期

关键词：

topology of textiles; knot theory; knot invariant; Kauffman polynomial; doubly-periodic interlaced structure;

D O I：

10.1177/0040517508096221

中图分类号：

TB3 [工程材料学]; TS1 [纺织工业、染整工业];

学科分类号：

0805 ; 080502 ; 0821 ;

摘要：

This paper is the second in the series on topological classification of textile structures. The classification problem can be resolved with the aid of invariants used in knot theory for classification of knots and links. Various numerical and polynomial invariants are considered in application to textile structures. A new Kauffman-type polynomial invariant is constructed for doubly-periodic textile structures. The values of the numerical and polynomial invariants are calculated for some simplest doubly-periodic interlaced structures and for some woven and knitted textiles.

引用

页码：822 / 836

页数：15

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