Implementation of the Habegger--Lin decision algorithm
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910224387932160 |
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| author | Kotorii, Yuka Mizusawa, Atsuhiko |
| author_facet | Kotorii, Yuka Mizusawa, Atsuhiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04433 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Implementation of the Habegger--Lin decision algorithm Kotorii, Yuka Mizusawa, Atsuhiko Geometric Topology 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. |
| title | Implementation of the Habegger--Lin decision algorithm |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2605.04433 |