A note on tunnel number of composite knots

Xutao Gao; Qilong Guo; Ruifeng Qiu

doi:10.1016/j.topol.2011.07.020

A note on tunnel number of composite knots

Xutao Gao
, Qilong Guo
, Ruifeng Qiu^*

^*此作品的通讯作者

数学科学学院

Dalian University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

Let K be a knot in a sphere S3. We denote by t(K) the tunnel number of K. For two knots K1 and K2, we denote by K1#K2 the connected sum of K1 and K2. In this paper, we will prove that if one of K1 and K2 has high distance while the other has distance at least 3 then t(K1#K2)=t(K1)+t(K2)+1.

源语言	英语
页（从-至）	2240-2243
页数	4
期刊	Topology and its Applications
卷	158
期	16
DOI	https://doi.org/10.1016/j.topol.2011.07.020
出版状态	已出版 - 1 10月 2011

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title = "A note on tunnel number of composite knots",

abstract = "Let K be a knot in a sphere S3. We denote by t(K) the tunnel number of K. For two knots K1 and K2, we denote by K1\#K2 the connected sum of K1 and K2. In this paper, we will prove that if one of K1 and K2 has high distance while the other has distance at least 3 then t(K1\#K2)=t(K1)+t(K2)+1.",

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author = "Xutao Gao and Qilong Guo and Ruifeng Qiu",

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AU - Gao, Xutao

AU - Guo, Qilong

AU - Qiu, Ruifeng

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N2 - Let K be a knot in a sphere S3. We denote by t(K) the tunnel number of K. For two knots K1 and K2, we denote by K1#K2 the connected sum of K1 and K2. In this paper, we will prove that if one of K1 and K2 has high distance while the other has distance at least 3 then t(K1#K2)=t(K1)+t(K2)+1.

AB - Let K be a knot in a sphere S3. We denote by t(K) the tunnel number of K. For two knots K1 and K2, we denote by K1#K2 the connected sum of K1 and K2. In this paper, we will prove that if one of K1 and K2 has high distance while the other has distance at least 3 then t(K1#K2)=t(K1)+t(K2)+1.

KW - Distance

KW - Heegaard splitting

KW - Tunnel

UR - https://www.scopus.com/pages/publications/80051792560

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DO - 10.1016/j.topol.2011.07.020

M3 - 文章

AN - SCOPUS:80051792560

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VL - 158

SP - 2240

EP - 2243

JO - Topology and its Applications

JF - Topology and its Applications

IS - 16

ER -

A note on tunnel number of composite knots

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