On tunnel number one links with surgeries yielding the 3-sphere
type: Item
instance of: scholarly article
title: On tunnel number one links with surgeries yielding the 3-sphere
zbMATH Open document ID: 1195.57015
author: Kai Ishihara
published in: Osaka Journal of Mathematics
publication date: 2010-04-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1266586792
review text: \textit{C.McA. Gordon} and \textit{J. Luecke} [J. Am. Math. Soc. 2, No.~2, 371--415 (1989; Zbl 0678.57005)] showed that knots are determined by their complements. That is, any non-trivial Dehn surgery on a non-trivial knot in the \(3\)-sphere does not yield the \(3\)-sphere. But there is a non-trivial link in the \(3\)-sphere which admits a non-trivial Dehn surgery yielding the \(3\)-sphere. A trivial example is a link having a trivial component or having a non-separating essential annulus in its exterior. Nontrivial examples of such links have been constructed. In particular, \textit{J. Berge} [Embedding the exteriors of one-tunnel knots and links in the \(3\)-sphere, unpublished manuscript] gave such examples of two component links which were tunnel number one. In the present paper, the author extends Berge's examples to construct infinitely many such tunnel number one links in the \(3\)-sphere.
reviewed by: Sangbum Cho
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 5692890
zbMATH Keywords: Tunnel number one links
zbMATH Keywords: Dehn surgery
zbMATH Keywords: Heegaard diagram
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5692890