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An algorithmic definition of Gabai width

Ricky Lee

Algebraic & Geometric Topology 23 (2023) 2415–2448
Abstract

We define the Wirtinger width of a knot and prove that this equals its Gabai width. This leads to an efficient technique for establishing upper bounds on Gabai width. We demonstrate an application of this technique by calculating the Gabai width of 54 756 tabulated prime 4–bridge knots. This is done by writing code for a special category of prime 4–bridge tabulated knots to get upper bounds on Gabai width via the Wirtinger width, then comparing with the theoretical lower bound on Gabai width for prime 4–bridge knots. We also provide results showing the advantages our methods have over the obvious method of obtaining upper bounds on Gabai width via planar projections.

Keywords
Gabai width
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 10 December 2019
Revised: 10 April 2022
Accepted: 15 May 2022
Published: 7 September 2023
Authors
Ricky Lee
Department of Mathematics
UC Santa Barbara
Goleta, CA
United States

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