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

School of Mathematical Sciences

Dalian University

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

4 Scopus citations

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.

Original language	English
Pages (from-to)	2240-2243
Number of pages	4
Journal	Topology and its Applications
Volume	158
Issue number	16
DOIs	https://doi.org/10.1016/j.topol.2011.07.020
State	Published - 1 Oct 2011

Keywords

Distance
Heegaard splitting
Tunnel

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10.1016/j.topol.2011.07.020

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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.",

keywords = "Distance, Heegaard splitting, Tunnel",

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

year = "2011",

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doi = "10.1016/j.topol.2011.07.020",

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T1 - A note on tunnel number of composite knots

AU - Gao, Xutao

AU - Guo, Qilong

AU - Qiu, Ruifeng

PY - 2011/10/1

Y1 - 2011/10/1

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

U2 - 10.1016/j.topol.2011.07.020

DO - 10.1016/j.topol.2011.07.020

M3 - 文章

AN - SCOPUS:80051792560

SN - 0166-8641

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

Abstract

Keywords

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