An algorithm to decide if a 3-manifold is a Haken manifold
type: Item
instance of: scholarly article
title: An algorithm to decide if a 3-manifold is a Haken manifold
zbMATH Open document ID: 0545.57003
DOI: 10.1016/0040-9383(84)90039-9
author: William Jaco
author: Ulrich Oertel
published in: Topology
publication date: 1984-01-01T00:00:00Z
review text: The authors develop an algorithm which determines whether a closed, irreducible 3-manifold M (given by a handle-decomposition) contains an injective surface \(F\neq S^ 2\) (i.e. \(\pi_ 1(F)\to \pi_ 1(M)\) is injective). In fact, if there are any injective surfaces in M this algorithm will actually produce one. An essential ingredient of the proof is \textit{W. Haken}'s classical theory of normal surfaces [Acta Math. 105, 245-375 (1961; Zbl 0100.194)].
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M35
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 3868241
zbMATH Keywords: incompressible surface
zbMATH Keywords: irreducible 3-manifold
zbMATH Keywords: handle-decomposition
zbMATH Keywords: injective surfaces
zbMATH Keywords: algorithm
zbMATH Keywords: normal surfaces
reviewed by: Dušan Repovš
MaRDI profile type: Publication
full work available at URL: 0040-9383(84)90039-9
OpenAlex ID: W1982860805
Wikidata QID: Q56172022
description: scientific article; zbMATH DE number 3868241