Vol. 15, No. 1, 2022

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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
Abstract

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.

Keywords
knot, tunnel number, computation, bridge number, SnapPy
Mathematical Subject Classification
Primary: 57K10, 57K31
Supplementary material

List of tunnel numbers

Milestones
Received: 8 November 2020
Revised: 20 July 2021
Accepted: 12 August 2021
Published: 14 March 2022

Communicated by Kenneth S. Berenhaut
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