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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
Lee, Ricky 1
@article{10_2140_agt_2023_23_2415,
author = {Lee, Ricky},
title = {An algorithmic definition of {Gabai} width},
journal = {Algebraic and Geometric Topology},
pages = {2415--2448},
publisher = {mathdoc},
volume = {23},
number = {6},
year = {2023},
doi = {10.2140/agt.2023.23.2415},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.2415/}
}
Lee, Ricky. An algorithmic definition of Gabai width. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2415-2448. doi: 10.2140/agt.2023.23.2415
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