Yarn Ball Knots and Faster Computations

TL;DR

This paper leverages the 3D structure of knots to reduce computational complexity in calculating knot invariants like linking numbers, outperforming traditional 2D diagram-based methods.

Contribution

It introduces a novel 3D approach to compute knot invariants more efficiently than existing 2D methods.

Findings

Significant reduction in computational complexity for knot invariants.

Applicable to a wide range of finite type invariants.

Demonstrates advantages over traditional diagram-based approaches.

Abstract

We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite type invariants. These savings are achieved in comparison with the 2D approach to knots using knot diagrams.