Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length≦k
Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length≦k
复制标题
对于具有长度≤k 的消失 Milnor 不变量的链接，长度为 2k+2 的 Milnor 不变量
DOI：
10.1016/j.topol.2015.01.003
复制
发表时间：
2015
影响因子：
0.6
通讯作者：
Yuka Kotorii and Akira Yasuhara
中科院分区：
文献类型：
--
作者：
Kazuhiro Hikami;Rei Inoue;Yuka Kotorii and Akira Yasuhara
J. - B。梅尔汉和第二作者证明了：如果所有长度≤ k的μ-不变量都为零，则长度在3 ~ 2k + 1之间的任何Milnor μ-不变量都可以表示为由链分支的带和得到的纽结的HOMFLYPT多项式的组合.他们还证明了他们的公式对于长度为2k + 2不成立。本文通过增加修正项，改进了他们的公式，给出了长度为2k + 2的μ ′-不变量.修正项可以通过由长度为k+ 1的μ ′-不变量确定的节点的HOMFLYPT多项式的组合来给出。特别地，对于任何4-分支链，长度为4的μ ′-不变量由我们的公式给出，因为所有长度为1的μ ′-不变量都为零。
J.-B. Meilhan and the second author showed that any Milnor μ¯-invariant of length between 3 and 2 k+ 1 can be represented as a combination of HOMFLYPT polynomial of knots obtained by certain band sum of the link components, if all μ¯-invariants of length≤ k vanish. They also showed that their formula does not hold for length 2 k+ 2. In this paper, we improve their formula to give the μ¯-invariants of length 2 k+ 2 by adding correction terms. The correction terms can be given by a combination of HOMFLYPT polynomial of knots determined by μ¯-invariants of length k+ 1. In particular, for any 4-component link the μ¯-invariants of length 4 are given by our formula, since all μ¯-invariants of length 1 vanish.