平面曲线，波前和勒让德结

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences Pub Date : 2001-07-15 DOI:10.1098/rsta.2001.0837

V. Goryunov

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引用次数: 4

摘要

本文综述了标准接触三维空间和实体环面中关于Legendrian节和连杆的一些最新研究结果。这包括有限阶不变量的描述和来自经典多项式连杆不变量的自连杆数的估计。我们还描述了由Chekanov和Pushkar引入的组合不变量，该组合不变量使他们能够证明Arnold关于平面上圆形锋面的一般形式中四顶点曲线的必要性的猜想。

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Plane curves, wavefronts and Legendrian knots

We survey some of the recent results on Legendrian knots and links in the standard contact 3–space and solid torus. These include the description of finite–order invariants and estimates of the self–linking number coming from the classical polynomial link invariants. We also describe the combinatorial invariant introduced by Chekanov and Pushkar, which allowed them to prove Arnold's conjecture on the necessity of four–cusp curves in generic eversions of a circular front in the plane.

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Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences

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