Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots
type: Item
instance of: scholarly article
title: Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots
zbMATH Open document ID: 1018.57003
DOI: 10.1016/S0166-8641(02)00100-1
author: Hyun-Jong Song
published in: Topology and its Applications
publication date: 2003-04-28T00:00:00Z
review text: The author introduces the concept of characteristic knots to \(\theta\)-curves with bridge decompositions. For a given knot \(K\) in \(S^3\), a tunnel is defined as an embedded arc in \(S^3\) with endpoints on \(K\) and interior disjoint from \(K\). A knot with an unknotting tunnel is called a tunnel-1 knot. By means of the refinement of Morimoto-Sakuma-Yokota's method of studying tunnel number one knots, another proof is provided for the tunnel number of the Montesinos knots dealt with by Klimenko-Sakuma.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1901912
zbMATH Keywords: Tunnel number one knot
zbMATH Keywords: \(\theta\)-curve
zbMATH Keywords: \({\mathbb Z}_2 \oplus {\mathbb Z}_2\)-branched covering
zbMATH Keywords: Heegaard decomposition
zbMATH Keywords: Montesinos knots
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
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full work available at URL: s0166-8641(02)00100-1
OpenAlex ID: W2026259872
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description: scientific article; zbMATH DE number 1901912