Involutions of knots that fix unknotting tunnels

被引：5

作者：

Futer, David ^{[1
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2007年 / 16卷 / 06期

关键词：

unknotting tunnel; two-bridge knot involution; handlebody;

D O I：

10.1142/S0218216507005506

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a knot that has an unknotting tunnel tau. We prove that K admits a strong involution that fixes tau pointwise if and only if K is a two-bridge knot and tau its upper or lower tunnel.

引用

页码：741 / 748

页数：8

共 50 条

[1] ON UNKNOTTING TUNNELS FOR KNOTS
MORIMOTO, K
SAKUMA, M
MATHEMATISCHE ANNALEN, 1991, 289 (01) : 143 - 167
[2] Genus one knots with unknotting tunnels and unknotting operations
Goda, H
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 1997, 6 (05) : 677 - 686
[3] KNOTS AND INVOLUTIONS
HARTLEY, R
MATHEMATISCHE ZEITSCHRIFT, 1980, 171 (02) : 175 - 185
[4] The length of unknotting tunnels
Cooper, Daryl
Lackenby, Marc
Purcell, Jessica S.
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2010, 10 (02): : 637 - 661
[5] Unknotting numbers of quasipositive knots
Tanaka, T
TOPOLOGY AND ITS APPLICATIONS, 1998, 88 (03) : 239 - 246
[6] Unknotting operations on knots and links
Shimizu, Ayaka
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2021, 30 (02)
[7] An unknotting sequence for torus knots
Siwach, V.
Madeti, P.
TOPOLOGY AND ITS APPLICATIONS, 2015, 196 : 668 - 674
[8] Unknotting sequences for torus knots
Baader, Sebastian
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2010, 148 : 111 - 116
[9] Unknotting genus one knots
Coward, Alexander
Lackenby, Marc
COMMENTARII MATHEMATICI HELVETICI, 2011, 86 (02) : 383 - 399
[10] An unknotting invariant for welded knots
A Gill
K Kaur
M Prabhakar
A Vesnin
Proceedings - Mathematical Sciences, 2021, 131

← 1 2 3 4 5 →