Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups
type: Item
instance of: scholarly article
title: Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups
zbMATH Open document ID: 1104.22005
author: Katsuya Eda
author: Vlasta Matijević
published in: Topology and its Applications
publication date: 2006-03-20T00:00:00Z
review text: These results generalize from dimension 1 to dimension 2 the second author's results on covering spaces of solenoids. Compact, connected 1-dimensional Abelian groups are constructed as inverse limits of circles. Compact, connected, 2-dimensional Abelian groups \(G\) are constructed as inverse limits of 2-dimensional tori. The authors reduce the problem of classifying finite \(s\)-sheeted covering spaces of such groups \(G\) to the classification of \(s\)-index torsionfree supergroups of the Pontryagin dual \(\widehat G\) of \(G\). This classification allows them to count the number of inequivalent covers in terms of the number theoretic properties of the entries in the \(2\times 2\) matrices that describe the bonding maps of the inverse limit.
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 57M10
Mathematics Subject Classification ID: 20K15
zbMATH DE Number: 5013521
zbMATH Keywords: compact group
zbMATH Keywords: compact Abelian group
zbMATH Keywords: 2-dimensional
zbMATH Keywords: finite-sheeted covering
reviewed by: James W. Cannon
MaRDI profile type: Publication
full work available at URL: j.topol.2005.02.005
OpenAlex ID: W2018651512
cites work: Torus-like continua which are not self-covering spaces
cites work: Classifying overlay structures of topological spaces
cites work: Classifying finite-sheeted covering mappings of paracompact spaces
cites work: Q5522742
DOI: 10.1016/J.TOPOL.2005.02.005
description: scientific article; zbMATH DE number 5013521