Symmetric surgery on asymmetric knots
type: Item
instance of: scholarly article
title: Symmetric surgery on asymmetric knots
zbMATH Open document ID: 0873.57005
author: Patrick J. Callahan
published in: Mathematische Annalen
publication date: 1997-07-06T00:00:00Z
review text: In their paper [ibid. 276, 323-340 (1987; Zbl 0624.57013)], \textit{M. Boileau}, \textit{F. Gonzalez-Acuña} and \textit{J. M. Montesinos} posed the question: Do there exist knots with no nontrivial symmetries which yield manifolds which are two-fold branched covers of the 3-sphere by nontrivial Dehn surgery. This question is answered in this paper by using techniques from hyperbolic geometry to construct an infinite family of knots with the required property.
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1031494
zbMATH Keywords: knots
zbMATH Keywords: symmetries
zbMATH Keywords: branched covers
zbMATH Keywords: hyperbolic
MaRDI profile type: Publication
full work available at URL: s002080050059
OpenAlex ID: W2062496343
DOI: 10.1007/S002080050059
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description: scientific article; zbMATH DE number 1031494