Implementation of the Habegger--Lin decision algorithm

Yuka Kotorii; Atsuhiko Mizusawa

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arXiv · 2605.04433

Implementation of the Habegger--Lin decision algorithm

Yuka Kotorii·Atsuhiko Mizusawa

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Abstract

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 $\overline{\mu}$-invariants.

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Yuka Kotorii, Atsuhiko Mizusawa. 2026-05-06. Implementation of the Habegger--Lin decision algorithm. https://arxiv.org/abs/2605.04433

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