A polynomial upper bound on Reidemeister moves for each link type
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915788618727424 |
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| author | Lackenby, Marc |
| author_facet | Lackenby, Marc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A polynomial upper bound on Reidemeister moves for each link type Lackenby, Marc Geometric Topology 57K10 (primary), 57K30, 68Q15 (secondary) 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. |
| title | A polynomial upper bound on Reidemeister moves for each link type |
| topic | Geometric Topology 57K10 (primary), 57K30, 68Q15 (secondary) |
| url | https://arxiv.org/abs/2602.09923 |