A diagrammatic approach to link invariants of finite degree
A diagrammatic approach to link invariants of finite degree
复制标题
链接有限度不变量的图解方法
DOI：
10.7146/math.scand.a-14444
复制
发表时间：
2004
影响因子：
0.5
通讯作者：
O. Östlund
中科院分区：
文献类型：
--
作者：
O. Östlund
M.Polyak和O.Viro在[5]中发展了Vassiliev链接不变量的图解公式的图解演算，并给出了低次不变量的几个显式公式。M.Goussarov[2]证明了这个箭图演算提供了所有Vassiliev纽结不变量的公式。原来的笔记[5]没有证据，也有一些微小的不准确之处。本文以一种独立的形式，用所有的证据和细节来填补文献[5]中的空白。此外，在基于一圈箭头图的代数上，引入了一种与节点的连通和相关的相容余代数结构。
In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev link invariants, and presented several explicit formulas for low degree invariants. M. Goussarov [2] proved that this arrow diagram calculus provides formulas for all Vassiliev knot invariants. The original note [5] contained no proofs, and it also contained some minor inaccuracies. This paper fills the gap in literature by presenting the material of [5] with all proofs and details, in a self-contained form. Furthermore, a compatible coalgebra structure, related to the connected sum of knots, is introduced on the algebra of based arrow diagrams with one circle.