Splitting Numbers of Links

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 complet...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 60; no. 3; pp. 587 - 614
Main Authors Cha, Jae Choon, Friedl, Stefan, Powell, Mark
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.08.2017
Subjects
Homology
Links
Lower bounds
Splitting
57N70
Alexander polynomial
covering links
57M27
Primary 57M25
splitting numbers of links
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Summary: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.
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ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091516000420