Representation of types and 3-manifolds.
type: Item
instance of: scholarly article
title: Representation of types and 3-manifolds.
zbMATH Open document ID: 1057.57013
author: Luis Valdez-Sanchez
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
full work available at URL: p11.xhtml
review text: If \(X\) is a connected compact orientable irreducible 3-manifold with torus boundary and \(r\) is a slope in \(\partial X\), then \(X(r)\) denotes the closed manifold obtained by Dehn-filling \(X\) along \(r\). If \(X\) is a knot exterior admitting two distinct planar boundary slopes \(r_1,r_2\), then at least one of the manifolds \(X(r_1), X(r_2)\) has a connected summand \(M\) with nontrivial torsion in first homology, as shown in [\textit{C. McA. Gordon}, Lectures at Knots '96, Ser. Knots Everything. 15, 263--290 (1997; Zbl 0940.57022)]. This summand \(M\) has special Heegaard splittings, whose structure is studied in this paper. In particular, the genus two case is classified, showing that no hyperbolic manifold can occur as \(M\).
reviewed by: Michele Mulazzani
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 2101095
zbMATH Keywords: Dehn-filling
zbMATH Keywords: Heegaard splitting
MaRDI profile type: Publication
OpenAlex ID: W2021094368
DOI: 10.2140/PJM.2003.210.367
description: scientific article; zbMATH DE number 2101095