A polynomial upper bound on Reidemeister moves

2013/02/01 by Lackenby, Marc · 2 citations
#57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1302.0180

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.

Cited by

• An elementary proof that linking problems are hard
• Rigidity of highly twisted plat diagrams

Related

• Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle
• Unknotting number and number of Reidemeister moves needed for unlinking
• An upper bound on Reidemeister moves
• Hard Diagrams of the Unknot
• The number of Reidemeister Moves Needed for Unknotting