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The tunnel
numbers of all 11- and 12-crossing alternating knots
Felipe Castellano-Macías and Nicholas Owad
Vol. 15 (2022), No. 1, 75–88
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Abstract |
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Using exhaustive techniques and results from Lackenby and many others, we compute the tunnel numbers of all 1655 alternating 11- and 12-crossing knots and of 881 nonalternating 11- and 12-crossing knots. We also find all 5525 Montesinos knots with 14 or fewer crossings. |
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Keywords
knot, tunnel number, computation, bridge number, SnapPy
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Mathematical Subject Classification
Primary: 57K10, 57K31
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Supplementary material |
Milestones
Received: 8 November 2020
Revised: 20 July 2021
Accepted: 12 August 2021
Published: 14 March 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Felipe Castellano-Macías | |
| Northeastern University Boston, MA United States |
Topology and Geometry of Manifolds
Unit Okinawa Institute of Science and Technology Graduate University Okinawa Japan |
| Nicholas Owad | |
| Department of Mathematics Hood College Frederick, MD United States |
Topology and Geometry of Manifolds
Unit Okinawa Institute of Science and Technology Graduate University Okinawa Japan |
