论文标题
八八八号电缆的彩色琼斯结多项式
The colored Jones polynomial of a cable of the figure-eight knot
论文作者
论文摘要
我们研究了$ n $二维有色的琼斯的渐近行为，该电缆的电缆多项式是$ \ exp（ξ/n）$的$ \ exp（ξ/n）$的渐近行为。我们表明，如果$ξ$足够大，那么当$ n $转到无限时，彩色琼斯多项式就会成倍增长。此外，增长率与与$ \ mathrm {sl}（2; \ Mathbb {r}）$表示相关的结外部的Chern-Simons不变。
We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial of a cable of the figure-eight knot, evaluated at $\exp(ξ/N)$ for a real number $ξ$. We show that if $ξ$ is sufficiently large, the colored Jones polynomial grows exponentially when $N$ goes to the infinity. Moreover the growth rate is related to the Chern-Simons invariant of the knot exterior associated with an $\mathrm{SL}(2;\mathbb{R})$ representation.
