First order invariants and cohomology of spaces of embeddings of self-intersecting curves into Rn
Date
2005-01-01
Authors
Advisors
Journal Title
Journal ISSN
ISSN
1468-4810
Volume Title
Publisher
Turpion Ltd.
Type
Article
Peer reviewed
Abstract
Description
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.
Keywords
RAE 2008, UoA 25 General Engineering and Mineral & Mining Engineering
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.