Involutions of irreducible 3-manifolds containing two-sided projective planes
type: Item
instance of: scholarly article
title: Involutions of irreducible 3-manifolds containing two-sided projective planes
zbMATH Open document ID: 0824.57008
DOI: 10.1016/0166-8641(94)90098-1
author: John Kalliongis
published in: Topology and its Applications
publication date: 1994-11-28T00:00:00Z
review text: The author analyzes involutions (periodic homeomorphisms with period 2) on compact irreducible sufficiently large 3-manifolds containing 2-sided projective planes. Two involutions \(f\) and \(g\) of a manifold \(M\) are said to be strongly equivalent (relative to \(\partial M)\), if there exists a homeomorphism \(k\) (which restricts to the identity on \(\partial M)\), such that \(kfk^{- 1} = g\) and \(k\) is isotopic to the identity (relative to \(\partial M)\). First he classifies the strongly equivalent classes of involutions on \(P \times I\) and a certain more complicated manifold. Then he shows that two involutions which induce the same outer automorphism of the fundamental group are strongly equivalent in the complement of a regular neighborhood of an invariant set of projective planes, and he analyzes how they differ in this regular neighborhood. He also shows that under certain conditions, isotopic involutions are strongly equivalent.
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 681629
zbMATH Keywords: projective plane
zbMATH Keywords: involutions
zbMATH Keywords: compact irreducible sufficiently large 3- manifolds containing 2-sided projective planes
zbMATH Keywords: automorphism of the fundamental group
zbMATH Keywords: invariant set of projective planes
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90098-1
OpenAlex ID: W1985449310
cites work: The \(\pi\)-orbifold group of a link
cites work: FINITE PRESENTATIONS OF GROUPS AND 3-MANIFOLDS
cites work: On $P^2$-irreducible 3-manifolds
cites work: Free Surfaces in S 3
cites work: Obstruction theory in 3-dimensional topology: classification theorems
cites work: Finitely presented subgroups of three-manifold groups
cites work: Q4743449
cites work: Involutions of nonirreducible 3-manifolds
cites work: ℤ2-equivariant hierarchies of irreducible 3-manifolds containing two-sided projective planes
cites work: Homeotopy groups of irreducible 3-manifolds which may contain two-sided projective planes
cites work: The Symmetries of Genus One Handlebodies
cites work: PL Involutions of Fibered 3-Manifolds
cites work: Splitting the PL involutions of nonprime 3-manifolds
cites work: PL Involutions of S 1 × S 1 × S 1
cites work: Q5724432
cites work: Homeomorphisms of 3-manifolds with compressible boundary
cites work: Finite group actions on 3-manifolds
cites work: On the involutions of closed surfaces
cites work: Cyclic actions on $S^2$- and $P^2$-bundles over $S^1$
cites work: The space of homeomorphisms of a 2-manifold
cites work: Projective planes in irreducible 3-manifolds
cites work: Involutions of sufficiently large 3-manifolds
cites work: On irreducible 3-manifolds which are sufficiently large
cites work: FINITE GROUP ACTIONS ON HAKEN 3-MANIFOLDS
description: scientific article; zbMATH DE number 681629