On the Alexander polynomial of lens space knots
type: Item
instance of: scholarly article
title: On the Alexander polynomial of lens space knots
zbMATH Open document ID: 1444.57008
author: Motoo Tange
published in: Topology and its Applications
publication date: 2020-04-07T00:00:00Z
review text: The author studies how the non-zero coefficient terms of the Alexander polynomial of lens space knots are distributed by defining the non-zero curve of a lens space knot. This curve is an embedding of several copies of \(\mathbb{R}\) into \(\mathbb{R}^2\). The author also introduces a new invariant called the \(\alpha\)-index that is useful in determining the Alexander polynomial of a lens space knot. Some other results in the paper give criteria for a lens space knot to have the Alexander polynomial of a torus knot.
Mathematics Subject Classification ID: 57K10
Mathematics Subject Classification ID: 57K14
zbMATH DE Number: 7187686
zbMATH Keywords: lens space surgery
zbMATH Keywords: Alexander polynomial
zbMATH Keywords: double-primitive knot
zbMATH Keywords: simple 1-bridge knot
zbMATH Keywords: \(L\)-space knots
zbMATH Keywords: torus knots
reviewed by: James Hebda
MaRDI profile type: Publication
full work available at URL: j.topol.2020.107124
OpenAlex ID: W3011882436
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DOI: 10.1016/J.TOPOL.2020.107124
description: scientific article; zbMATH DE number 7187686