On Gusarov's groups of knots
On Gusarov's groups of knots
复制标题
论古萨罗夫的结群
DOI：
10.1017/s030500419800303x
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发表时间：
1999
影响因子：
0.8
通讯作者：
T. Stanford
中科院分区：
文献类型：
--
作者：
K. Ng;T. Stanford
给出了一个基于纯辫子交换子的纽结的Gusarov群[Gscr]n的构造，并证明了[Gscr]n的任意元素都由无限多个辫子指数小于或等于n+1的素数交错纽结表示.我们还研究了[Gscr]n的无挠部分[Vscr]n，它是不能用小于或等于n的任何有理Vassiliev不变量来区分的纽结的等价类群.推广了n-平凡的Gusarov-Ohyama定义，给出了任意群的下中心级数的第n群元的刻划.
We give a construction of Gusarov's groups [Gscr ]n of knots based on pure braid commutators, and show that any element of [Gscr ]n is represented by an infinite number of prime alternating knots of braid index less than or equal to n+1. We also study [Vscr ]n, the torsion-free part of [Gscr ]n, which is the group of equivalence classes of knots which cannot be distinguished by any rational Vassiliev invariant of order less than or equal to n. Generalizing the Gusarov–Ohyama definition of n-triviality, we give a characterization of the elements of the nth group of the lower central series of an arbitrary group.