Automatic Evaluation of the Links–Gould Invariant for all Prime Knots of up to 10 Crossings
Automatic Evaluation of the Links–Gould Invariant for all Prime Knots of up to 10 Crossings
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自动评估链接 - 最多 10 个交叉点的所有素结的古尔德不变量
DOI：
10.1142/s0218216500000153
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发表时间：
1999
影响因子：
0.5
通讯作者：
D. D. Wit
中科院分区：
文献类型：
--
作者：
D. D. Wit
本文描述了一种自动评估任何链接的 Links-Gould 二变量多项式链接不变量 (LG) 的方法，仅给出编织表示。该方法目前对于评估链接的 LG 是可行的，对于该链接，我们有最多 5 个字符串索引的辫子表示。数据提供了不变量、最多 10 个交叉的所有素结和各种其他链接。 LG 区分这些链接，并检测手性链接的手性。从这个意义上说，它比著名的二变量 HOMFLY 和 Kauffman 多项式更敏感。有趣的是，当应用于击败 HOMFLY 不变量的示例时，LG“几乎”失败了。自动方法实际上适用于评估任何此类状态和不变量，已为其确定适当的 R 矩阵以及帽和杯矩阵。
This paper describes a method for the automatic evaluation of the Links–Gould two-variable polynomial link invariant (LG) for any link, given only a braid presentation. This method is currently feasible for the evaluation of LG for links for which we have a braid presentation of string index at most 5. Data are presented for the invariant, for all prime knots of up to 10 crossings and various other links. LG distinguishes between these links, and also detects the chirality of those that are chiral. In this sense, it is more sensitive than the well-known two-variable HOMFLY and Kauffman polynomials. When applied to examples which defeat the HOMFLY invariant, interestingly, LG 'almost' fails. The automatic method is in fact applicable to the evaluation of any such state sum invariant for which an appropriate R matrix and cap and cup matrices have been determined.