About some infinite family of 2-bridge knots and 3-manifolds
type: Item
instance of: scholarly article
title: About some infinite family of 2-bridge knots and 3-manifolds
zbMATH Open document ID: 0963.57003
DOI: 10.1155/S0161171200003422
author: Yangkok Kim
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2001-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/48785
review text: The author studies the topological and algebraic properties of some series of cyclically presented groups which arise as fundamental groups of closed connected orientable 3-manifolds. These manifolds are presented by polyhedron schemata, that is, they are obtained by pairwise identifications of polygons in special tessellations of the boundary of a 3-ball. Then the author proves that the considered manifolds are cyclic coverings of the 3-sphere branched along the 2-bridge knots \((k+1)_2\) or \((k+1)_1\), according as \(k\) is even or odd, respectively. Finally, it is also shown that these manifolds are 2-fold branched coverings of the 3-sphere branched over special \(n\)-periodic knots.
reviewed by: Alberto Cavicchioli
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1529553
zbMATH Keywords: branched coverings
zbMATH Keywords: maximally symmetric manifolds
zbMATH Keywords: cyclically presented groups
zbMATH Keywords: 2-bridge knots
MaRDI profile type: Publication
OpenAlex ID: W2122999691
description: scientific article; zbMATH DE number 1529553