A polynomial upper bound on Reidemeister moves

Marc Lackenby

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arXiv · 1302.0180

A polynomial upper bound on Reidemeister moves

Marc Lackenby

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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.

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Marc Lackenby. 2013-02-01. A polynomial upper bound on Reidemeister moves. https://arxiv.org/abs/1302.0180

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