Finite-type invariants detecting the mutant knots
Finite-type invariants detecting the mutant knots
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检测突变结的有限型不变量
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Murakami
中科院分区：
文献类型：
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作者：
J. Murakami
有限型不变量的概念是由Gusarov [2]引入的，然后出现在Vassiliev [8]关于多项式映射逼近的纽结空间的某些0同调的工作中。Kontsevich [3]利用弦图和迭代积分给出了所有有限型不变量的统一描述。在本文中，我们表明，没有有限型不变量的程度小于11区分突变结。一个11度的有限型不变量，它可以区分一些突变的结构造如下。设QK（q）是对应于量子包络代数Uq（sl ~ 4）的分划（2，1）表示的纽结K的量子不变量。设KC为康威11交叉结，KKT为Kinoshita-Terasaka结，而©为平凡结。然后，利用M. Ochiai [7]，我们有QKC（q）-QKKT（q）Q©（q）=
The notion of finite-type invariants was introduced by Gusarov [2] and then appeared in the work of Vassiliev [8] concerning to certain 0homology of the space of knots approimated by polynomial mappings. Kontsevich [3] gives a universal description for all the finite-type invariants by using chord diagrams and iterated integral. In this paper, we show that there is no finite-type invariant of degree less than 11 which distinguishes mutant knots. A finite-type invariant of degree 11 which can distinguish some mutant knots is constructed as follows. Let QK(q) be the quantum invariant of a knot K corresponding to the representation of the partition (2,1) of the quantum enveloping algebra Uq(sl4). Let KC be the Conway’s 11-crossing knot, KKT be the Kinoshita-Terasaka knot, and © be the trivial knot. Then, by using the computer software “KnotTheoryByComputer” by M. Ochiai [7], we have QKC (q)−QKKT (q) Q©(q) =