Scissor equivalence for torus links
type: Item
instance of: scholarly article
title: Scissor equivalence for torus links
zbMATH Open document ID: 1253.57003
author: Sebastian Baader
published in: Bulletin of the London Mathematical Society
publication date: 2012-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.0876
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 6092636
zbMATH Keywords: torus link
zbMATH Keywords: signature
zbMATH Keywords: cobordism distance
MaRDI profile type: Publication
OpenAlex ID: W1972803630
arXiv ID: 1011.0876
DOI: 10.1112/BLMS/BDS044
review text: Given two oriented links in \(S^3\), consider all smooth cobordisms between the two links in \(S^3 \times [0,1]\) with no closed components. The cobordism distance between the two links is defined to be the absolute value of the maximal Euler characteristic of such a cobordism. The main result of this paper is to find, up to a bounded multiplicative error, the cobordism distance between two torus links, apart from an explicit set of exceptions. The expression for the distance is in terms of the genus and signature of each of the two links.NEWLINENEWLINEThe proof makes use of the Thom Conjecture, and also a result of \textit{C. McA. Gordon, R. A. Litherland} and \textit{K. Murasugi} [Can. J. Math. 33, 381--394 (1981; Zbl 0469.57004)]. In addition, various explicit cobordisms are given. These are built using two types of scissor cobordism (smoothing and saddle moves).
reviewed by: Jessica Banks
description: scientific article; zbMATH DE number 6092636