Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold
type: Item
instance of: scholarly article
title: Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold
zbMATH Open document ID: 1078.57017
DOI: 10.2478/BF02476541
author: Masahito Toda
published in: Central European Journal of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: The author studies the first homology of finite regular branched coverings of a universal Borromean orbifold. The main result of the paper gives a criterion for when an irreducible representation of a finite covering transformation group \(G\) is an irreducible component of the first homology if \(G\) has certain symmetries. This provides also information on the first Betti number of finite coverings of general 3-manifolds. The investigation is motivated by a problem (raised by Thurston) in 3-dimensional topology, namely, does any 3-manifold with infinite fundamental group have a finite-sheeted cover with positive first Betti number?
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 2143692
zbMATH Keywords: 3-manifold
zbMATH Keywords: Betti number
zbMATH Keywords: hyperbolic geometry
reviewed by: Changchang Xi
MaRDI profile type: Publication
cites work: Q3927897
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cites work: Three dimensional manifolds, Kleinian groups and hyperbolic geometry
full work available at URL: https://doi.org/10.2478/bf02476541
OpenAlex ID: W1996569507
description: scientific article; zbMATH DE number 2143692