Representing links in 3-manifolds by branched coverings of \(S^3\)
type: Item
instance of: scholarly article
title: Representing links in 3-manifolds by branched coverings of \(S^3\)
zbMATH Open document ID: 0906.57002
author: Michele Mulazzani
author: Riccardo Piergallini
published in: Manuscripta Mathematica
publication date: 1998-11-29T00:00:00Z
review text: The authors introduce a combinatorial representation by means of planar colored diagrams of links in closed 3-manifolds described as branched coverings of the 3-sphere. Then they prove an equivalence theorem based on local moves on the diagrams, and obtain a universal configuration for such a representation. As a consequence, they give unified proofs of two different results on existence of fibered links in 3-manifolds, and finally extend two results obtained respectively by \textit{J. Harer} [Math. Proc. Camb. Philos. Soc. 92, 133-138 (1982; Zbl 0501.57004)] for knots and by \textit{J. R. Stallings} [Algebr. geom. Topol., Stanford/Calif. 1976, Proc. Symp. pure Math., Vol. 32, Part 2, 55-60 (1978; Zbl 0394.57007)] for links in the 3-sphere.
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1215546
zbMATH Keywords: colored diagram representation of a link
zbMATH Keywords: branched coverings
zbMATH Keywords: universal branch sets
zbMATH Keywords: fibered links
reviewed by: Alberto Cavicchioli
MaRDI profile type: Publication
full work available at URL: s002290050081
OpenAlex ID: W2013122449
DOI: 10.1007/S002290050081
description: scientific article; zbMATH DE number 1215546