An upper bound on Reidemeister moves

TL;DR

This paper establishes an explicit upper limit on the number of Reidemeister moves needed to transform one link diagram into another, simplifying the process of determining link equivalence.

Contribution

It introduces a concrete upper bound on Reidemeister moves, offering a straightforward approach to solving the link equivalence problem.

Findings

Derived an explicit upper bound for Reidemeister moves

Simplified the link equivalence problem

Provided a practical method for link diagram transformations

Abstract

We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links.