Small difference between tunnel numbers of cable knots and their companions

Junhua Wang; Wenjie Diao; Yanqing Zou

doi:10.1016/j.topol.2024.109058

Small difference between tunnel numbers of cable knots and their companions

Junhua Wang^*
, Wenjie Diao
, Yanqing Zou

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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].

Original language	English
Article number	109058
Journal	Topology and its Applications
Volume	357
DOIs	https://doi.org/10.1016/j.topol.2024.109058
State	Published - 1 Nov 2024

Keywords

Cable knot
Primitive knot
Tunnel number

Access to Document

10.1016/j.topol.2024.109058

Cite this

@article{58f90d6320174f52b2b434080612a58f,

title = "Small difference between tunnel numbers of cable knots and their companions",

abstract = "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].",

keywords = "Cable knot, Primitive knot, Tunnel number",

author = "Junhua Wang and Wenjie Diao and Yanqing Zou",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier B.V.",

year = "2024",

month = nov,

day = "1",

doi = "10.1016/j.topol.2024.109058",

language = "英语",

volume = "357",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Small difference between tunnel numbers of cable knots and their companions

AU - Wang, Junhua

AU - Diao, Wenjie

AU - Zou, Yanqing

PY - 2024/11/1

Y1 - 2024/11/1

N2 - 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].

AB - 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].

KW - Cable knot

KW - Primitive knot

KW - Tunnel number

UR - https://www.scopus.com/pages/publications/85203544063

U2 - 10.1016/j.topol.2024.109058

DO - 10.1016/j.topol.2024.109058

M3 - 文章

AN - SCOPUS:85203544063

SN - 0166-8641

VL - 357

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 109058

ER -

Small difference between tunnel numbers of cable knots and their companions

Abstract

Keywords

Access to Document

Other files and links

Cite this