An algorithm to find ribbon disks for alternating knots

Owens, B. and Swenton, F. (2023) An algorithm to find ribbon disks for alternating knots. Experimental Mathematics, (doi: 10.1080/10586458.2022.2158968) (Early Online Publication)

Abstract

We describe an algorithm to find ribbon disks for alternating knots, and the results of a computer implementation of this algorithm. The algorithm is underlain by a slice link obstruction coming from Donaldson’s diagonalization theorem. It successfully finds ribbon disks for slice two-bridge knots and for the connected sum of any alternating knot with its reverse mirror, as well as for 662,903 prime alternating knots of 21 or fewer crossings. We also identify some examples of ribbon alternating knots for which the algorithm fails to find ribbon disks, though a related search identifies all such examples known. Combining these searches with known obstructions, we resolve the sliceness of all but 3276 of the over 1.2 billion prime alternating knots with 21 or fewer crossings.

• Item Type: Articles
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Owens, Professor Brendan
• Authors: Owens, B., and Swenton, F.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Experimental Mathematics
• Publisher: Taylor & Francis
• ISSN: 1058-6458
• ISSN (Online): 1944-950X
• Published Online: 15 March 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Experimental Mathematics 2023
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
165275		Alternating links and cobordism groups	Brendan Owens	Engineering and Physical Sciences Research Council (EPSRC)	EP/I033754/1	M&S - Mathematics