On unknotting tunnels for knots
type: Item
instance of: scholarly article
title: On unknotting tunnels for knots
zbMATH Open document ID: 0697.57002
DOI: 10.1007/BF01446565
author: Kanji Morimoto
author: Makoto Sakuma
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164774
review text: The main purpose of this paper is to determine the non-simple knots in \(S^ 3\) with tunnel number one, and to classify the unknotting tunnels for them. Roughly speaking, such knots are certain satellites of torus knots via 2-bridge links; and most of them admit precisely 4 (infinitely many resp.) unknotting tunnels up to homeomorphism (isotopy resp.). To understand the unknotting tunnels for them, we introduce concepts of a dual tunnel and a (1,1)-tunnel, and we also review the unknotting tunnels for torus knots and 2-bridge knots from this view point. To detect inequivalences of the unknotting tunnels for non-simple knots, we use a very natural homotopy invariant; and we also classify the (known) unknotting tunnels for torus knots and 2-bridge knots through the invariant.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4143045
zbMATH Keywords: non-simple knots in \(S^ 3\) with tunnel number one
zbMATH Keywords: unknotting tunnels
zbMATH Keywords: satellites of torus knots via 2-bridge links
MaRDI profile type: Publication
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OpenAlex ID: W1984733792
description: scientific article; zbMATH DE number 4143045