Towards a Classification of Knots

TL;DR

This paper explores the potential for finite algorithms to classify knots, presenting two promising approaches: one using planar projections and another employing cubic lattice placements.

Contribution

It introduces two novel algorithmic approaches for knot classification, advancing the understanding of computational methods in knot theory.

Findings

Two promising algorithms for knot classification are proposed.

The approaches are based on knot projections and cubic lattice placements.

Further research is needed to establish algorithmic completeness.

Abstract

We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on placing knots on a cubic lattice.