Cusp volumes of alternating knots
type: Item
instance of: scholarly article
title: Cusp volumes of alternating knots
zbMATH Open document ID: 1378.57011
author: Marc Lackenby
author: Jessica S. Purcell
published in: Geometry \& Topology
publication date: 2016-09-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1410.6297
reviewed by: Kazuhiro Ichihara
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 6628600
zbMATH Keywords: alternating
zbMATH Keywords: knot
zbMATH Keywords: cusp
zbMATH Keywords: volume
MaRDI profile type: Publication
OpenAlex ID: W3098666589
arXiv ID: 1410.6297
DOI: 10.2140/GT.2016.20.2053
review text: In the paper under review, the authors show that the area of the boundary of the maximal cusp for a hyperbolic alternating knot can be bounded above and below by a linear function of the twist number of an alternating diagram of the knot. NEWLINENEWLINEAs a corollary, diagrammatic estimates on Euclidean lengths of slopes for such knots are given. This implies that, for any closed 3-manifold with sufficiently large Gromov norm, there are at most finitely many prime alternating knots such that the manifold is obtained by Dehn surgery along the knot. Also it is implied that there is a universal lower bound on the cusp density of hyperbolic alternating knots.
description: scientific article; zbMATH DE number 6628600