论文标题
在用于椭圆奇点链接的规范多项式上
On a canonical polynomial for links of elliptic singularities
论文作者
论文摘要
规范多项式是与正常表面奇异性相关的多变量拓扑庞加莱序列的重要输出。可以将其视为Seiberg的多变量多项式概括 - 链接的不变。在椭圆细菌的情况下，考虑了另一个关键的拓扑不变式，即椭圆序列，它反映了椭圆细菌的特定结构并指导其几种特性。 在本说明中，我们研究了这两个对象的关系。首先，我们描述了规范多项式指数的结构，并证明它们决定了椭圆序列。对于相反的问题，我们通过自然扩展其图来考虑椭圆细菌的感应设置，并比较相应的指数集。这导致了良好扩展的定义，该定义可以以相应规范多项式的包含类型公式为特征。这以兼容的方式反映了椭圆序列的“标志结构”。
The canonical polynomial is an important output of the multivariable topological Poincaré series associated with a normal surface singularity. It can be considered as a multivariable polynomial generalization of the Seiberg--Witten invariant of the link. In the case of elliptic germs, another key topological invariant was considered, the elliptic sequence, which mirrors the specific structure of the elliptic germs and guides several properties of them. In this note we study the relationship of these two objects. First of all, we describe the structure of the exponents of the canonical polynomial and prove that they determine the elliptic sequence. For the converse problem, we consider an inductive setup of elliptic germs via natural extension of their graphs and compare the corresponding sets of exponents. This leads to the definition of a good extension which can be characterized by an inclusion type formula for the corresponding canonical polynomials. This reflects in a compatible way the `flag structure' of the elliptic sequence.
