PL equivariant surgery and invariant decompositions of 3-manifolds
type: Item
instance of: scholarly article
title: PL equivariant surgery and invariant decompositions of 3-manifolds
zbMATH Open document ID: 0682.57005
DOI: 10.1016/0001-8708(89)90067-4
author: William Jaco
author: J. Hyam Rubinstein
published in: Advances in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Normal surface theory was introduced by W. Haken to show the existence of hierarchies for certain 3-manifolds M (``Haken-manifolds''). The authors study least weight surfaces, i.e. normal surfaces with minimal intersections with the 1-skeleton of a fixed triangulation of M. The main applications are constructive PL proofs of results which were previously obtained by Meeks-Yau via minimal surface theory. Specifically, let G be a group of simplicial homeomorphisms of M. The authors give PL proofs for (1) the Equivariant Sphere Theorem, (2) the existence of a G-invariant prime decomposition of M (if G is finite and M has no closed 1-handles), (3) the existence of a G-invariant characteristic submanifold V of a Haken-manifold M (if G is finite and M is not a torus bundle over \(S^ 1\) with V a neighborhood of the fiber).
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 4117466
zbMATH Keywords: hierarchies
zbMATH Keywords: Haken-manifolds
zbMATH Keywords: least weight surfaces
zbMATH Keywords: normal surfaces
zbMATH Keywords: Equivariant Sphere Theorem
zbMATH Keywords: G-invariant prime decomposition
zbMATH Keywords: G-invariant characteristic submanifold
Wikidata QID: Q29397743
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
full work available at URL: 0001-8708(89)90067-4
OpenAlex ID: W2080541323
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description: scientific article; zbMATH DE number 4117466