论文标题
通过Chern-simons扰动理论的流量的Vassiliev不变
Vassiliev Invariants for Flows Via Chern-Simons Perturbation Theory
论文作者
论文摘要
Chern-Simons量规理论的扰动扩展导致结和链接的不变性，有限的类型不变性或Vassiliev不变性。已经证明，在扰动理论的任何顺序上，由此产生的表达是该顺序的不变性。在当前上下文中介绍了配置空间上的BOTT-TAUBES积分，以在扰动理论中以几何和拓扑设置以给定的顺序编写Feynman图。配置空间形式主义的后果之一是，由此产生的幅度以同学术语给出。这种共同体结构可用于将bott-taubes积分转换为Chern-Simons扰动振幅，反之亦然。在本文中，该程序在耦合常数中最多执行三阶。这扩大了瑟斯顿以前已经完成的一些工作。最后，我们利用这些结果将其纳入形式主义中，在$ 3 $ - manifold上平滑而无脱水的矢量领域。获得的Bott-Taubes积分用于构建扩展Komendarczyk和Volić工作的高阶渐近Vassiliev不变式。
The perturbative expansion of Chern-Simons gauge theory leads to invariants of knots and links, the finite type invariants or Vassiliev invariants. It has been proven that at any order in perturbation theory the resulting expression is an invariant of that order. Bott-Taubes integrals on configuration spaces are introduced in the present context to write Feynman diagrams at a given order in perturbation theory in a geometrical and topological setting. One of the consequences of the configuration space formalism is that the resulting amplitudes are given in cohomological terms. This cohomological structure can be used to translate Bott-Taubes integrals into Chern-Simons perturbative amplitudes and vice versa. In this article this program is performed up to third order in the coupling constant. This expands some work previously worked out by Thurston. Finally we take advantage of these results to incorporate in the formalism a smooth and divergenceless vector field on the $3$-manifold. The Bott-Taubes integrals obtained are used for constructing higher-order asymptotic Vassiliev invariants extending the work of Komendarczyk and Volić.
