An Algorithmic Definition of Gabai Width

TL;DR

This paper introduces the Wirtinger width, proves its equivalence to Gabai width, and presents an efficient algorithmic method to compute it, successfully calculating the Gabai width for around 50,000 knots.

Contribution

The paper defines Wirtinger width, shows it equals Gabai width, and develops an efficient algorithmic approach for computing Gabai width.

Findings

Wirtinger width equals Gabai width for knots

An efficient algorithmic technique for bounding Gabai width

Calculated Gabai width for approximately 50,000 knots

Abstract

We define the Wirtinger width of a knot. Then we prove the Wirtinger width of a knot equals its Gabai width. The algorithmic nature of the Wirtinger width leads to an efficient technique for establishing upper bounds on Gabai width. As an application, we use this technique to calculate the Gabai width of approximately 50000 tabulated knots.