A polynomial upper bound on Reidemeister moves
Geometric Topology
2014-12-12 v2
Abstract
We prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)^{11} Reidemeister moves. Moreover, every diagram in this sequence has at most (7 c)^2 crossings. We also prove a similar theorem for split links, which provides a polynomial upper bound on the number of Reidemeister moves required to transform a diagram of the link into a disconnected diagram.
Keywords
Cite
@article{arxiv.1302.0180,
title = {A polynomial upper bound on Reidemeister moves},
author = {Marc Lackenby},
journal= {arXiv preprint arXiv:1302.0180},
year = {2014}
}
Comments
62 pages, 34 figures. Final version; to appear in the Annals of Mathematics