Homology of spaces of knots in any dimensions
First calculations of cohomology classes (including zero-dimensional classes, i.e. the numerical invariants of knots) of spaces of knots in Euclidean spaces are presented, and combinatorial expressions for these classes are given. A deep analogy between the topological theory of knot spaces and the theory of arrangements of planes is indicated and exploited. This original paper demonstrates international excellence in fundamental research and will make a significant impact on the advancement of academic research in topology.
Citation : Vassiliev, V. (2001) Homology of Spaces of Knots in Any Dimensions. Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences, 359(1784), pp. 1343-1364.
ISSN : 1471-2962
Research Group : Textiles Engineering and Materials (TEAM)