Splitting Numbers of Links

Cha, Jae Choon; Friedl, Stefan; Powell, Mark

doi:10.1017/s0013091516000420

Splitting Numbers of Links

Cha, Jae Choon; Friedl, Stefan; Powell, Mark

Authors

Jae Choon Cha

Stefan Friedl

Mark Powell

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 9 or fewer crossings. Also, with these techniques, we either reprove or improve upon the lower bounds for splitting numbers of links computed by J. Batson and C. Seed using Khovanov homology.

Citation

Cha, J. C., Friedl, S., & Powell, M. (2017). Splitting Numbers of Links. Proceedings of the Edinburgh Mathematical Society, 60(03), 587-614. https://doi.org/10.1017/s0013091516000420

Journal Article Type	Article
Online Publication Date	Jan 3, 2017
Publication Date	Aug 1, 2017
Deposit Date	Oct 3, 2017
Publicly Available Date	Oct 4, 2017
Journal	Proceedings of the Edinburgh Mathematical Society
Print ISSN	0013-0915
Electronic ISSN	1464-3839
Publisher	Cambridge University Press
Peer Reviewed	Peer Reviewed
Volume	60
Issue	03
Pages	587-614
DOI	https://doi.org/10.1017/s0013091516000420
Related Public URLs	https://arxiv.org/abs/1308.5638

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Copyright Statement
This article has been published in a revised form in Proceedings of the Edinburgh Mathematical Society https://doi.org/10.1017/S0013091516000420. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Edinburgh Mathematical Society 2017.