Vassiliev invariants and the Hopf algebra of chord diagrams

被引:8
|
作者
Willerton, S
机构
[1] Department of Mathematics and Statistics, University of Edinburgh, Edinburgh EHd 3JZ, King's Buildings
关键词
D O I
10.1017/S0305004100073965
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper is closely related to Bar-Natan's work, and fills in some of the gaps in [1]. Folio-wing his analogy of the extension of knot invariants to knots with double points to the notion of multivariate calculus on polynomials, we introduce a new notation which facilitates the formulation of a Leibniz type formula for the product of two Vassiliev invariants. This leads us to see how Bar-Natan's co-product of chord diagrams corresponds to multiplication of Vassiliev invariants. We also include a proof that the multiplication in A is a consequence of Bar-Natan's 4T relation. The last part of this paper consists of a proof that the space of weight systems isa sub-Hopf algebra of the space A*, by means of the canonical projection.
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页码:55 / 65
页数:11
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