Surgery on double knots and symmetries
type: Item
instance of: scholarly article
title: Surgery on double knots and symmetries
zbMATH Open document ID: 0624.57013
DOI: 10.1007/BF01450747
author: José María Montesinos-Amilibia
author: Michel Boileau
author: F. González-Acuña
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164202
review text: This paper studies symmetries (i.e. homeomorphisms of finite order) of 3- manifolds obtained by Dehn surgeries on a double of a noninvertible knot, and shows that these manifolds admit no nontrivial symmetry except for a finite number of surgeries. Moreover, it determines when these manifolds are 2-fold branched covers of \(S^ 3\); this gives the exact range of validity of the conjecture of Whitten that ``no manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of \(S^ 3\)''.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 4013543
zbMATH Keywords: symmetries of 3-manifolds
zbMATH Keywords: Dehn surgeries on a double of a noninvertible knot
zbMATH Keywords: 2-fold branched covers of \(S^ 3\)
reviewed by: Makoto Sakuma
MaRDI profile type: Publication
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OpenAlex ID: W1984095197
description: scientific article; zbMATH DE number 4013543