Habegger-Lin决定算法的实现
Implementation of the Habegger--Lin decision algorithm
AI总结：
本文实现了Habegger-Lin决定算法，展示了新的无法通过Milnor链接同伦不变量区分的链接对，并提供了算法实现代码。
摘要：
Habegger和Lin给出了基于字符串链接模某些群作用的链接同伦类分类。作为应用，他们构造了一个判断给定两个链接是否同伦的算法。在\cite{KM4}中，我们明确计算了4和5组分情况下的这些群作用。因此，Habegger-Lin算法可以有效应用于这些情况。在本文中，我们呈现了该算法的实现，该实现可在\cite{KMcode}获得，并展示了新的链接对，这些链接不具有同伦关系，但无法通过Milnor的链接同伦不变量区分，称为$\overlineμ$-不变量。
英文摘要：
Habegger and Lin gave a classification of link-homotopy classes of links in terms of that of string links modulo certain group actions. As an application, they constructed an algorithm for determining whether given two links are link-homotopic. In \cite{KM4}, we explicitly computed these group actions for the 4- and 5-component cases. Consequently, the Habegger--Lin algorithm can be effectively applied in these cases. In this paper, we present an implementation of this algorithm, which is available at \cite{KMcode}, and exhibit new pairs of links that are not link-homotopic yet cannot be distinguished by Milnor's link-homotopy invariants, called $\overlineμ$-invariants.
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