Equivariant annulus theorem for 3-manifolds
type: Item
instance of: scholarly article
title: Equivariant annulus theorem for 3-manifolds
zbMATH Open document ID: 0569.57023
author: Tsuyoshi Kobayashi
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: The author uses an existence theorem of equivariant annuli to construct a simple example of a 3-manifold admitting no finite group action. More precisely, consider two prime knots \(K_ 1\) and \(K_ 2\) with nonhomeomorphic exteriors, such that \(K_ 1\) is not strongly negative amphicheiral and \(K_ 2\) is not strongly invertible; then the exterior of the connected sum \(K_ 1\#K_ 2\) admits no finite group action.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 3909361
zbMATH Keywords: 3-manifold without finite group actions
zbMATH Keywords: equivariant annuli
zbMATH Keywords: prime knots
zbMATH Keywords: strongly negative amphicheiral
zbMATH Keywords: strongly invertible
reviewed by: Francis Bonahon
MaRDI profile type: Publication
full work available at URL: pjaa.59.403
OpenAlex ID: W2093032202
cites work: Q5658847
cites work: Least area incompressible surfaces in 3-manifolds
cites work: Q4114528
cites work: Q3871581
cites work: Seifert fibered spaces in 3-manifolds
cites work: Multiply connected minimal surfaces and the geometric annulus theorem
cites work: Correction to "Closed 3-Manifolds with No Periodic Maps"
cites work: Q4107635
cites work: Q3888190
DOI: 10.3792/PJAA.59.403
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description: scientific article; zbMATH DE number 3909361