Legendrian solid-torus links
Legendrian solid-torus links
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勒让德实体环面链接
DOI：
10.4310/jsg.2004.v2.n3.a6
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发表时间：
2004
影响因子：
0.7
通讯作者：
L. Traynor
中科院分区：
文献类型：
--
作者：
Lenhard L. Ng;L. Traynor
在圆的1-射流空间中构造了Legendrian连杆的微分渐变代数不变量。与r3的理论类似，庞加莱-契卡诺夫多项式和特征代数也可以与这样的连杆联系起来。该理论被应用于区分各种结，以及作为理性缠结的Legendrian版本闭包的链接。对于大量的双分量环节，庞加莱-契卡诺夫多项式符合生成函数理论所定义的多项式。给出了结点和连杆的例子，它们具有相同的多项式，但具有不同的特征代数，它们的水平类型为偶数。用Legendrian卫星构造得到的结果与DGA和生成函数技术得到的结果进行了比较。
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R 3 , Poincare-Chekanov polynomials and characteristic al- gebras can be associated to such links. The theory is applied to dis- tinguish various knots, as well as links that are closures of Legendrian versions of rational tangles. For a large number of two-component links, the Poincare-Chekanov polynomials agree with the polynomials defined through the theory of generating functions. Examples are given of knots and links which differ by an even number of horizontal flypes that have the same polynomials but distinct characteristic algebras. Results ob- tainable from a Legendrian satellite construction are compared to results obtainable from the DGA and generating function techniques.