纽结的Alexander Fitting理想的Gröbner基
Gröbner Bases for Alexander Fitting Ideals of Links
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中文总结 AI 辅助
针对多变量Alexander理论生成的无优选生成元的Fitting理想，固定系数域与单项序后，通过多项式收缩的简约Gröbner基表示这些理想得到纽结的Alexander-Gröbner不变量，还推导了行列式-除子互反性并计算了多种纽结的相关不变量。
中文摘要 AI 辅助
多变量Alexander理论会产生没有优选生成元的Fitting理想。在固定系数域和单项序后，我们通过这些理想的多项式收缩的简约Gröbner基来表示它们，从而得到纽结的Alexander-Gröbner不变量。在有理数域\\\\(\mathbb Q\\\\
英文摘要
Multivariable Alexander theory produces Fitting ideals without preferred generators. After fixing a coefficient field and a monomial order, we represent these ideals by reduced Gröbner bases of their polynomial contractions, obtaining Alexander--Gröbner invariants of links. Over \(\mathbb Q\), for the maximal free-abelian coefficient system of a connected compact oriented \(3\)-manifold whose nonempty boundary is a disjoint union of tori, we deduce determinant-divisor reciprocity from Blanchfield duality. We compute these invariants for torus links and low-crossing links, and we determine \(\AG_2\) for a two-component pretzel family.
