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Splitting Numbers of Links

Part of: Topological manifolds Low-dimensional topology

Published online by Cambridge University Press:  03 January 2017

Jae Choon Cha ,
Stefan Friedl  and
Mark Powell
Jae Choon Cha
Affiliation:
Department of Mathematics, POSTECH, Pohang 790–784, Republic of Korea (jccha@postech.ac.kr) School of Mathematics, Korea Institute for Advanced Study, Seoul 130–722, Republic of Korea
Stefan Friedl
Affiliation:
Mathematisches Institut, Universität zu Köln, 50931 Köln, Germany (sfriedl@gmail.com)
Mark Powell
Affiliation:
Département de Mathématiques, Université du Québec à Montréal, Montréal, QC, Canada (mark@cirget.ca)
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Abstract

The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the splitting numbers of links with nine or fewer crossings. Also, with these techniques, we either reprove or improve upon the lower bounds for splitting numbers of links computed by Batson and Seed using Khovanov homology.

Keywords

splitting numbers of linkscovering linksAlexander polynomial

MSC classification

Secondary: 57M25: Knots and links in $S^3$ 57M27: Invariants of knots and 3-manifolds 57N70: Cobordism and concordance
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 587 - 614
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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