# Yarn ball knots and faster computations

## TL;DR

This paper shows how using 3D representations of knots can lead to faster computations of knot invariants compared to traditional 2D methods.

## Contribution

The novel contribution is leveraging 3D knot structures to reduce computational complexity for calculating knot invariants.

## Key findings

- 3D knot representations offer computational savings over 2D diagrams for invariants like the linking number.
- Finite type invariants can be computed more efficiently using 3D approaches.
- The 3D method is generally applicable to a wide range of knot invariants.

## 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.