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

Textile Research Journal

Volumn 79, Issue 9, 2009, Pages 822-836

  Grishanov, S ^a   Meshkov, V ^b   Omelchenko, A ^b  

^a DE MONTFORT UNIVERSITY   (United Kingdom)

^b PETER THE GREAT ST PETERSBURG POLYTECHNIC UNIVERSITY   (Russian Federation)

Author keywords

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

Indexed keywords

GRAPH THEORY; POLYNOMIALS; TEXTILES;

DOUBLY PERIODIC; INTERLACED STRUCTURE; KNOT INVARIANTS; KNOT THEORY; POLYNOMIAL INVARIANTS; TEXTILE STRUCTURES; TOPOLOGICAL CLASSIFICATION; TOPOLOGICAL INVARIANTS;

WEAVING;

CLASSIFICATION; KNITTED FABRIC; KNOT; MATHEMATICAL ANALYSIS; STRUCTURAL ANALYSIS; WOVEN FABRIC;

EID: 66649133856     PISSN: 00405175     EISSN: None     Source Type: Journal    
DOI: 10.1177/0040517508096221     Document Type: Article

References (10)

1. Grishanov, S.A., Meshkov, V.R., and Omelchenko, A.V., A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods, Textil. Res. J., (2007).
2. Prasolov, V.V., and Sossinsky, A.B., “Knots, Links, Braids and 3-manifolds: An Introduction to the New Invariants in Low-dimensional Topology”, American Mathematical Society, Providence, RI, USA, 1997.
3. Cromwell, P.R., “Knots and Links”, Cambridge University Press, Cambridge, 2004, 350 pp.
4. Kauffman, L.H., “Knots and Physics”, 2nd edn., World Scientific, London, UK, 1993.
5. Vassiliev, V.A., Cohomology of Knot Spaces. Theory of Singularities and its Applications. Adv. Soviet Math., 1, 23-70 (1990).
6. Atiyah, M., “The Geometry and Physics of Knots”, Cambridge University Press, Cambridge, 1999, 78 pp.
7. Grishanov, S.A., Meshkov, V.R., and Omelchenko, A.V., Kauffman-type Polynomial Invariants for Doubly-periodic Structures, J. Knot Theor. Ramif., 16(6), 779-788 (2007).
8. Emery, I., “The Primary Structures of Fabrics: An Illustrated Classification”, Thames & Hudson, London, 1994.
9. Grishanov, S.A., Meshkov, V.R., and Vassiliev, V.A., On Finite Type Invariants of Textile Structures, Accepted in J. Knot Theor. Ramif., 2007.
10. Dowson, R.M., Enumeration and Identification by Elimination of Weave Families of Given Repeat Size, Textil. Res. J., 70, 304-310 (2000).