On football manifolds of E. Molnár
type: Item
instance of: scholarly article
title: On football manifolds of E. Molnár
zbMATH Open document ID: 1224.57002
author: Alberto Cavicchioli
author: A. I. Telloni
published in: Acta Mathematica Hungarica
publication date: 2011-02-08T00:00:00Z
review text: \textit{E. Molnár} [Differential geometry and its applications, Proc. Conf., Dubrovnik/Yugosl. 1988, 217--241 (1989; Zbl 0694.57007)] studied compact orientable hyperbolic 3-manifolds obtained by face identification of certain solids. They are known as hyperbolic football manifolds \(M = \mathbb H^3 /G\), \(M' =\mathbb H^3 /G'\); the isometry groups \(G\) and \(G'\) are given explicitly by finite presentations. The authors show that these presentations are induced by genus 2 Heegard diagrams of \(M\) and \(M'\), that is, they are geometric. Furthermore, it is shown that \(M\) and \(M'\) are ``hyperelliptic'' which means that they permit an involution with quotient space \(S^3\). Moreover, \(M\) and \(M'\) are 2-fold coverings of \(S^3\) branched along certain 3-bridge links which are determined. Further, hyperbolic 3-manifolds are proved to be hyperelliptic.
reviewed by: Gerhard Burde
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 5848543
zbMATH Keywords: hyperelliptic manifolds
zbMATH Keywords: hyperbolic 3-manifold
zbMATH Keywords: cyclic coverings
zbMATH Keywords: links
zbMATH Keywords: isometry groups
zbMATH Keywords: football manifold
describes a project that uses: SnapPea
MaRDI profile type: Publication
full work available at URL: s10474-009-8196-9
OpenAlex ID: W2036100811
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DOI: 10.1007/S10474-009-8196-9
description: scientific article; zbMATH DE number 5848543