Integral geometry of plane curves and knot invariants
Integral geometry of plane curves and knot invariants
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平面曲线的积分几何和结不变量
DOI：
10.4310/jdg/1214458740
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发表时间：
1994
影响因子：
2.5
通讯作者：
Zhenghan Wang
中科院分区：
文献类型：
--
作者：
Xiaoxia Lin;Zhenghan Wang
研究了与纽结相关的维滕的Chern-Simons路径积分的微扰展开式中作为第二系数的纽结不变量的积分表达式。其中一个积分是经典Crofton积分在凸平面曲线上的推广，它与Arnold最近定义的一般平面曲线的不变量有关，具有辛几何和接触几何的深刻动机.这些平面曲线不变量的二次边界推导出使用它们的关系与结不变量。
We study the integral expression of a knot invariant obtained as the second coefficient in the perturbative expansion of Witten's Chern-Simons path integral associated with a knot. One of the integrals involved turns out to be a generalization of the classical Crofton integral on convex plane curves, and it is related with the invariants of generic plane curves recently defined by Arnold, with deep motivations in symplectic and contact geometry. Quadratic bounds on these plane curve invariants are derived using their relationship with the knot invariant.