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Splitting numbers and signatures


Authors: David Cimasoni, Anthony Conway and Kleopatra Zacharova
Journal: Proc. Amer. Math. Soc. 144 (2016), 5443-5455
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/proc/13156
Published electronically: June 17, 2016
MathSciNet review: 3556285
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Abstract: The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. We obtain a lower bound on the splitting number in terms of the (multivariable) signature and nullity. Although very elementary and easy to compute, this bound turns out to be suprisingly efficient. In particular, it makes it a routine check to recover the splitting number of 129 out of the 130 prime links with at most 9 crossings. Also, we easily determine 16 of the 17 splitting numbers that were studied by Batson and Seed using Khovanov homology, and later computed by Cha, Friedl and Powell using a variety of techniques. Finally, we determine the splitting number of a large class of 2-bridge links which includes examples recently computed by Borodzik and Gorsky using a Heegaard Floer theoretical criterion.


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Additional Information

David Cimasoni
Affiliation: Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
Email: david.cimasoni@unige.ch

Anthony Conway
Affiliation: Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
Email: anthony.conway@unige.ch

Kleopatra Zacharova
Affiliation: Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
Email: kleopatra.zacharova@etu.unige.ch

DOI: https://doi.org/10.1090/proc/13156
Received by editor(s): February 4, 2016
Received by editor(s) in revised form: February 15, 2016
Published electronically: June 17, 2016
Communicated by: David Futer
Article copyright: © Copyright 2016 American Mathematical Society