Splitting numbers of links
Jae Choon Cha, Stefan Friedl, and Mark Powell
TL;DR
This paper introduces new techniques involving covering links and Alexander invariants to compute the splitting number of links, providing complete results for links with up to nine crossings and refining existing bounds from Khovanov homology.
Contribution
The paper presents novel methods for calculating the splitting number of links, advancing the computational tools in link theory.
Findings
Complete determination of splitting numbers for links with ≤9 crossings
Reproving and improving bounds for splitting numbers using new techniques
Enhanced understanding of link splitting through algebraic invariants
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology