First order invariants and cohomology of spaces of embeddings of self-intersecting curves into Rn
Knot invariants are numerical characteristics of knots (in particular, of textile structures) reflecting their major geometrical properties. Their combinatorial formulae enable simple algorithms to be designed for obtaining these characteristics directly from the pictures of knots. This work provides first essential results on the existence of integral characteristic formulae (in contrast to fractional ones). In particular, it describes the first essential obstruction to and a criterion of the existence of such formulae. It opens a new approach to this problem, based on advanced methods of algebraic topology, and provides means to explore this problem in full depth.
Citation : Vassiliev, V. (2005) First Order Invariants and Cohomology of Spaces of Embeddings of Self-intersecting Curves into Rn. Izvestiya Mathematics, 69(5), pp. 865-912.
ISSN : 1468-4810
Research Group : Textiles Engineering and Materials (TEAM)