The nonuniqueness of Chekanov polynomials of Legendrian knots
The nonuniqueness of Chekanov polynomials of Legendrian knots
复制标题
勒让德结的切卡诺夫多项式的非唯一性
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Sumana Shrestha
中科院分区：
文献类型：
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作者：
P. Melvin;Sumana Shrestha
例子给出了总理勒让德结在标准的接触3-空间，有任意多个不同的Chekanov多项式，驳斥了一个猜想的伦尼吴。这些是使用新的“Legendrian tangle replacement”技术构建的。这种技术，然后使用表明，多个Chekanov多项式的现象，实际上是很常见的。最后，在Yufa和Branson未发表的工作的基础上，给出了Legendrian前沿的列表，沿着他们的Chekanov多项式，代表最大的Thurston-Bennequin Legendrian结，每种结类型的9个或更少的交叉。这些结是成对的，使得任何结的镜像的正面以标准方式通过旋转结的正面来获得。
Examples are given of prime Legendrian knots in the standard contact 3-space that have arbitrarily many distinct Chekanov polynomials, refuting a conjecture of Lenny Ng. These are constructed using a new "Legendrian tangle replacement" technique. This technique is then used to show that the phenomenon of multiple Chekanov polynomials is in fact quite common. Finally, building on unpublished work of Yufa and Branson, a tabulation is given of Legendrian fronts, along with their Chekanov polynomials, representing maximal Thurston-Bennequin Legendrian knots for each knot type of nine or fewer crossings. These knots are paired so that the front for the mirror of any knot is obtained in a standard way by rotating the front for the knot.