Orders and actions of branched coverings of hyperbolic links
type: Item
instance of: scholarly article
title: Orders and actions of branched coverings of hyperbolic links
zbMATH Open document ID: 1167.57001
published in: Topology and its Applications
publication date: 2009-05-28T00:00:00Z
review text: Let \(M\), \(M'\) be compact oriented 3-manifolds. Let \(L'\subset M'\) be a nonempty link and \(G\) a group that acts orientation-preservingly on \(M\) such that the natural projection \(p:M\to M/G\cong M'\) is a branched covering with branch set \(L'\). The pre-image of \(L'\) in \(M\) is a link \(L\). If the stabilizer of each point \(x\in L = p^{-1}(L')\) equals the covering group \(G\) then \(p\) is called \textit{strongly branched}. The author proves the following: Let \(M\), \(M'\) be compact oriented 3-manifolds whose boundary is a (possible empty) disjoint union of tori. Let \(L'\subset M'\) be a prime link. If the exterior of \(L'\) in \(M'\) is irreducible and its JSJ (Jaco-Shalen-Johannson) decomposition contains a hyperbolic piece, then there exists at most one positive integer \(d\) for which \(M\) is a \(d\)-fold covering of \(M'\), strongly branched over \(L'\). Moreover if \(N'\) is an integral homology 3-sphere and \(L'\) is a hyperbolic link, then for any manifold \(M\) any two cyclic coverings \(p_1,p_2:M\to M'\) over \(L'\), of prime degrees, are conjugate.
reviewed by: Claus Ernst
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 5558960
zbMATH Keywords: group actions
zbMATH Keywords: strongly branched covering
zbMATH Keywords: orbifold
zbMATH Keywords: hyperbolic volume
author: António Salgueiro
MaRDI profile type: Publication
full work available at URL: j.topol.2009.01.014
OpenAlex ID: W2108839805
cites work: Lectures on hyperbolic geometry
cites work: Spherical space forms and Dehn filling
cites work: The characteristic toric splitting of irreducible compact 3-orbifolds
cites work: Q5658847
cites work: Rigidity of geometrically finite hyperbolic cone-manifolds
cites work: Q3802262
cites work: Nonfibering Spherical 3-Orbifolds
cites work: Q4314557
cites work: Volume and bounded cohomology
cites work: Q3924842
cites work: Homotopy equivalences of 3-manifolds with boundaries
cites work: Q4877326
cites work: Manifold covers of 3-orbifolds with geometric pieces
cites work: Regenerating hyperbolic and spherical cone structures from Euclidean ones
cites work: Q4314293
cites work: Hyperbolic links and cyclic branched coverings
cites work: ORDERS OF BRANCHED COVERINGS OF LINKS
cites work: Knoten mit zwei Brücken
cites work: The Geometries of 3-Manifolds
cites work: Transformation Groups and Natural Bundles
DOI: 10.1016/J.TOPOL.2009.01.014
Recommended article: ORDERS OF BRANCHED COVERINGS OF LINKS
Recommended article: On cyclic branched coverings of hyperbolic links
Recommended article: Hyperbolic links and cyclic branched coverings
Recommended article: On $p$ -fold cyclic branched coverings of hyperbolic links
Recommended article: On the degrees of branched coverings over links
Recommended article: Hyperbolic 2-fold branched coverings of links and their quotients.
Recommended article: Q4799224
Recommended article: Hyperbolic knots and cyclic branched covers
Recommended article: On the Branch Points in the Branched Coverings of Links
Recommended article: Branched covers of quasi‐positive links and L‐spaces
description: scientific article; zbMATH DE number 5558960