Essential laminations and Dehn surgery on 2-bridge knots
type: Item
instance of: scholarly article
title: Essential laminations and Dehn surgery on 2-bridge knots
zbMATH Open document ID: 0873.57007
DOI: 10.1016/0166-8641(95)00085-U
published in: Topology and its Applications
publication date: 1997-11-02T00:00:00Z
review text: The main result of the paper is that any nontrivial Dehn surgery on a nontorus 2-bridge knot produces a manifold which is covered by \(\mathbb{R}^3\). In particular, his manifold is irreducible and has infinite fundamental group. As a consequence, the author recovers the classical theorem of \textit{Moto-o Takahashi} [Two-bridge knots have property \(P\), Mem. Am. Math. Soc. 239 (1981; Zbl 0451.57003)] that 2-bridge knots satisfy property \(P\). The results of the paper are consequences of showing that the considered manifolds contain an essential lamination. The results of the paper were also obtained independently by \textit{Ramin Naimi} [Contemp. Math. 164, 183-186 (1994; Zbl 0819.57002)].
reviewed by: Józef H. Przytycki
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 768749
zbMATH Keywords: Dehn surgery
zbMATH Keywords: 2-bridge knot
zbMATH Keywords: fundamental group
zbMATH Keywords: essential lamination
author: Charles I. Delman
MaRDI profile type: Publication
cites work: Essential laminations in Seifert-fibered spaces
cites work: Surgery on knots in solid tori
cites work: Pseudo-Anosov maps and surgery on fibred 2-bridge knots
cites work: Essential laminations in 3-manifolds
cites work: Incompressible surfaces in 2-bridge knot complements
cites work: Closed incompressible surfaces in alternating knot and link complements
cites work: Elementary surgery along a torus knot
cites work: Constructing essential laminations in 2-bridge knot surgered 3-manifolds
cites work: Two-bridge knots have property 𝑃
Wikidata QID: Q127570017
description: scientific article; zbMATH DE number 768749