Dehn fillings of 3-manifolds and non-persistent tori
type: Item
instance of: scholarly article
title: Dehn fillings of 3-manifolds and non-persistent tori
zbMATH Open document ID: 0935.57024
DOI: 10.1016/S0166-8641(99)00038-3
author: Luis Valdez-Sanchez
published in: Topology and its Applications
publication date: 1999-11-23T00:00:00Z
review text: The main result of this paper is that a compact, connected, orientable, irreducible 3-manifold \(M\) with incompressible torus boundary with a planar boundary slope \(r\) either contains essential tori of special type or the manifold \(M(r)\) obtained by Dehn filling is small (is a connected sum of two pieces of the form \(S^3\), \(S^1\times S^2\), or a lens space). This result may be applied to give a condition under which a knot in \(S^3\) is cabled. It also shows that if \(M\) is the exterior of a knot in \(S^3\) with \(r\) a slope of \(\partial M\) and \(M(r)\) is reducible, then at most one of its prime factors is not a lens space.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1367573
zbMATH Keywords: cabled knot
MaRDI profile type: Publication
Recommended article: Toroidal Dehn fillings on hyperbolic 3-manifolds
Recommended article: Nonhyperbolic Dehn fillings on hyperbolic \(3\)-manifolds
Recommended article: Dehn filling hyperbolic 3-manifolds
Recommended article: Toroidal Dehn filling on large hyperbolic 3-manifolds
Recommended article: Dehn fillings on a two torus boundary components 3-manifold
Recommended article: Reducible and toroidal 3-manifolds obtained by Dehn fillings
Recommended article: Q5454071
Recommended article: Dehn fillings of large hyperbolic 3-manifolds
Recommended article: Reducing and toroidal Dehn fillings on 3-manifolds bounded by two tori
Recommended article: Dehn filling, reducible 3-manifolds, and Klein bottles
description: scientific article; zbMATH DE number 1367573