论文标题
$ u_q（SL（2）） - $ Quantum不变性通过嵌入的Lagrangians的交集统一
$U_q(sl(2))-$quantum invariants unified via intersections of embedded Lagrangians
论文作者
论文摘要
在本文中，我们证明了$ u_q（sl（2））$ Quantum不变性的统一模型，这是通过嵌入式Lagrangians在配置空间中的交叉点进行的。更具体地说，我们构造了刺穿圆盘}中配置空间中拉格朗日交叉点的{\ em状态总和，这在三个变量中是多项式。它通过系数的专业化，{\ em恢复了彩色的琼斯多项式和彩色的亚历山大多项式}。该公式适用于用量子组相同表示的定向链接，并且可以在统一的根部进行评估。作为推论，琼斯和亚历山大多项式既作为嵌入式lagrangians}在配置空间中的嵌入式lagrangians}之间的相交配对的{\ em empecorizatization，这适用于计算。特别是，我们从dunctured Disc中的{\ em arcs and Circles}给出的子序列之间的相交中获得了琼斯多项式的{\ em第一个相交模型。
In this paper we prove a unified model for $U_q(sl(2))$ quantum invariants through intersections of embedded Lagrangians in configuration spaces. More specifically, we construct a {\em state sum of Lagrangian intersections in the configuration space in the punctured disc}, which is a polynomial in three variables. It {\em recovers the coloured Jones polynomial and the coloured Alexander polynomial} through specialisations of coefficients. This formula works for oriented links coloured with the same representation of the quantum group and can be evaluated at roots of unity. As a corollary, the Jones and Alexander polynomials come both as {\em specialisations of an intersection pairing between embedded Lagrangians} in configuration spaces, which is suitable for computations. In particular, we obtain the {\em first intersection model for the Jones polynomial} from intersections between submanifolds which are given by {\em arcs and circles} in the punctured disc.
