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arXiv · 2602.09923

A polynomial upper bound on Reidemeister moves for each link type

Marc Lackenby
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Abstract

For each link type $K$ in the 3-sphere, we show that there is a polynomial $p_K$ such that any two diagrams of $K$ with $c_1$ and $c_2$ crossings differ by at most $p_K(c_1) + p_K(c_2)$ Reidemeister moves. As a consequence, the problem of recognising whether a given link diagram represents $K$ is in the complexity class NP and hence can be completed deterministically in exponential time. We calculate this polynomial $p_K$ explicitly for various classes of links.

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Marc Lackenby. 2026-02-10. A polynomial upper bound on Reidemeister moves for each link type. https://arxiv.org/abs/2602.09923

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