Generating function polynomials for legendrian links
Generating function polynomials for legendrian links
复制标题
生成传奇链接的函数多项式
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
L. Traynor
中科院分区：
文献类型：
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作者：
L. Traynor
结果表明，在圆的 1{jet 空间中，产生拓扑等价链接的交换和飞行过程可以产生非等价传奇链接。所考虑的链接的每个组成部分都是 0{ 函数的 1{jet 的传奇同位素，因此不能通过经典旋转数或 Thurston{Bennequin 不变量来区分。通过通过生成函数理论计算由与链接相关联的同源群定义的不变多项式来区分链接。这些生成函数多项式的许多计算支持这样的信念：这些多项式携带与切卡诺夫一阶多项式的改进版本相同的信息，该多项式是通过全纯曲线理论定义的。
It is shown that, in the 1{jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1{jet of the 0{function, and thus cannot be distinguished by the classical rotation number or Thurston{Bennequin invariants. The links are distinguished by calculating invariant polynomials dened via homology groups associated to the links through the theory of generating functions. The many calculations of these generating function polynomials support the belief that these polynomials carry the same information as a rened version of Chekanov’s rst order polynomials which are dened via the theory of holomorphic curves.