Classification of free actions of finite groups on the 3-torus
type: Item
instance of: scholarly article
title: Classification of free actions of finite groups on the 3-torus
zbMATH Open document ID: 1001.57035
DOI: 10.1016/S0166-8641(01)00090-6
author: Ku Yong Ha
author: Jang Hyun Jo
author: Seung Won Kim
author: Jong Bum Lee
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: Classifying free actions of finite groups on the 3-torus, up to topological conjugacy, is reduced to classifying all normal free Abelian subgroups of affine Bieberbach groups with finite quotients, up to affine conjugacy. In this paper, the authors give a complete classification of such groups using Lee-Shin-Yokura's method [\textit{K. B. Lee, J. Shin} and \textit{S. Yokura}, ibid. 53, No. 2, 153-175 (1993; Zbl 0817.57029)]. Some cases were worked out in detail in this paper and the other cases were stated only. The authors work out the other cases in detail in part II [JP J. Geom. Topol. 1, No. 1, 111-133 (2001; Zbl 1001.57034), see above].
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1787539
zbMATH Keywords: group actions
zbMATH Keywords: Bieberbach groups
zbMATH Keywords: affine conjugacy
MaRDI profile type: Publication
cites work: Q3128821
cites work: On $P^2$-irreducible 3-manifolds
cites work: Almost sufficiently large Seifert fiber spaces
cites work: Free Cyclic Actions on S 1 × S 1 × S 1
cites work: Free actions of finite Abelian groups on the 3-torus
full work available at URL: s0166-8641(01)00090-6
OpenAlex ID: W2100143911
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description: scientific article; zbMATH DE number 1787539