Splitting numbers and signatures
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- by David Cimasoni, Anthony Conway and Kleopatra Zacharova PDF
- Proc. Amer. Math. Soc. 144 (2016), 5443-5455 Request permission
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.References
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Additional Information
- David Cimasoni
- Affiliation: Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
- MR Author ID: 677173
- Email: david.cimasoni@unige.ch
- Anthony Conway
- Affiliation: Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
- MR Author ID: 1181487
- 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
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5443-5455
- MSC (2010): Primary 57M25
- DOI: https://doi.org/10.1090/proc/13156
- MathSciNet review: 3556285