On universal hyperbolic orbifold structures in \(S^3\) with the Borromean rings as singularity
type: Item
instance of: scholarly article
title: On universal hyperbolic orbifold structures in \(S^3\) with the Borromean rings as singularity
zbMATH Open document ID: 1227.57006
author: Hugh Michael Hilden
author: José María Montesinos-Amilibia
author: María Teresa Lozano Imízcoz
published in: Hiroshima Mathematical Journal
publication date: 2011-03-30T00:00:00Z
review text: Denote by \(B\) the Borromean rings. Let \(a\), \(b\) and \(c\) be the components of \(B\). The main result of the paper is Theorem~1. Given integers \(r\geq 3\), \(p\geq 2\), \(q\geq 2\), every \(3\)-manifold \(M^3\) is a covering \(M^3 \to S^3\) over \(B\) such that the branching indices upon \(a\) are \(\{1,2,2p\}\), upon \(b\) are \(\{1,2,2q\}\), and upon \(c\) are all \(r\). As a corollary, we have that the hyperbolic orbifold \(\mathbf{B}_{r,2p,2q}\), \(r\geq 3\), \(p\geq 2\), \(q\geq 2\), is universal.
reviewed by: Samyon R. Nasyrov
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 5872136
zbMATH Keywords: orbifold
zbMATH Keywords: Borromean rings
zbMATH Keywords: universal orbifold
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1291818850
OpenAlex ID: W1512996075
DOI: 10.32917/HMJ/1291818850
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description: scientific article; zbMATH DE number 5872136