Small difference between tunnel numbers of cable knots and their companions

Small difference between tunnel numbers of cable knots and their companions

We prove that for any nontrivial knot K⊂S3 and a p/q-cable knot K⋆ of K, the tunnel number t(K)=t(K⋆) if and only if K is p/q-primitive. This result solves a problem mentioned in [8].

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Veröffentlicht in:Topology and its applications 2024-11, Vol.357, p.109058, Article 109058
Hauptverfasser: Wang, Junhua, Diao, Wenjie, Zou, Yanqing
Format: Artikel
Sprache:eng
Schlagworte:
Cable knot
Primitive knot
Tunnel number
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Zusammenfassung:We prove that for any nontrivial knot K⊂S3 and a p/q-cable knot K⋆ of K, the tunnel number t(K)=t(K⋆) if and only if K is p/q-primitive. This result solves a problem mentioned in [8].
ISSN:0166-8641
DOI:10.1016/j.topol.2024.109058