A polynomial upper bound on Reidemeister moves for each link type

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Marc Lackenby
DOI: 10.48550/arxiv.2602.09923
Cited by: 0

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.

Fields of Study & Subjects

Geometric and Algebraic Topology Advanced Graph Theory Research Complexity and Algorithms in Graphs

Publication details

Journal / source
arXiv (Cornell University)
Publication date
10 February 2026
Language
EN
Document type
Preprint