The coloured Jones function
The coloured Jones function
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有色琼斯函数
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
H. Morton
中科院分区：
文献类型：
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作者：
P. Melvin;H. Morton
由维度 k 的不可约 SU(2)q 模着色的框架结 K 的不变量 JK,k 通过通用 R 矩阵研究为 k 的函数。结果表明，当JK,k写成幂级数inh且q=eh时，hd的系数是次数最多为2d+1的奇多项式ink。该系数是 K 的瓦西里耶夫不变量。论文的第二部分表明，ask 是变化的，这些不变量跨越了框架结的所有度数 Vassiliev 不变量空间的 ad 维子空间。还研究了无框架结的类似问题。
The invariantsJK,k of a framed knotK coloured by the irreducibleSU(2)q-module of dimensionk are studied as a function ofk by means of the universalR-matrix. It is shown that whenJK,k is written as a power series inh withq=eh, the coefficient ofhd is an odd polynomial ink of degree at most 2d+1. This coefficient is a Vassiliev invariant ofK. In the second part of the paper it is shown that ask varies, these invariants span ad-dimensional subspace of the space of all Vassiliev invariants of degreed for framed knots. The analogous questions for unframed knots are also studied.