Combinatorial formulas for cohomology of spaces of knots
A general method of constructing combinatorial formulas detecting non-equivalence of knots in R3 is invented and demonstrated on the simplest example. The method is based on the study of the discriminant space, consisting of singular knots. A generalization of these formulas is able to identify or separate textile structures, i.e. double periodic knots and links. This generalization, together with concrete calculations, is a part of the current work on characterizing textile structures by topological methods. This method will be used by the textile scientists in the studies of structure-property relationship of textiles.
Citation : Vassiliev, V. (2004) Combinatorial Formulas for Cohomology of Spaces of Knots. In: Bryden, J.M., eds. Advances in topological quantam field, IOS Press and Kluwer Academic Publishers in conjunction with the NATO Scientific Affairs Divisiontheory, pp. 1-21.
ISBN : 1-4020-2771-0
Research Group : Textiles Engineering and Materials (TEAM)