Networking Seifert surgeries on knots. II: The Berge's lens surgeries
type: Item
instance of: scholarly article
title: Networking Seifert surgeries on knots. II: The Berge's lens surgeries
zbMATH Open document ID: 1179.57009
author: Arnaud Deruelle
author: Katura Miyazaki
author: Kimihiko Motegi
published in: Topology and its Applications
publication date: 2009-04-03T00:00:00Z
review text: In an unpublished manuscript ``Networking Seifert surgeries on knots'' (available on the third author's webpage), the authors defined a 1-dimensional complex whose vertices are Seifert surgeries; that is, Dehn surgeries on a knot in the 3-sphere resulting in Seifert fiber spaces. A Seifert for a Seifert surgery is a trivial knot in the 3-sphere that becomes a fiber in the resulting Seifert fiber space. Two vertices of the complex are connected by an edge if one is obtained from the other by twisting along a Seifert. The complex is called the Seifert surgery network. The present paper is concerned with surgeries that yield lens spaces. J. Berge, in an unpublished manuscript from 1990, gave a list of twelve infinite families of such surgeries and it has been conjectured that the list is complete [cf. \textit{C. McA. Gordon}, Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 631--642 (1991; Zbl 0743.57008)]. The authors show that any surgery on Berge's list can be obtained from a Seifert surgery on a torus knot by twisting along at most two Seiferts.
reviewed by: Bruce Hughes
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 5539530
zbMATH Keywords: Dehn surgery
zbMATH Keywords: lens space
zbMATH Keywords: Berge knot
zbMATH Keywords: Seifert fibration
MaRDI profile type: Publication
full work available at URL: j.topol.2008.10.012
OpenAlex ID: W2004895486
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DOI: 10.1016/J.TOPOL.2008.10.012
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description: scientific article; zbMATH DE number 5539530