Every Reidemeister move is needed for each knot type

2004/04/07 by Tobias Hagge, Tobias J. Hagge, Hagge, Tobias J. · 1 citation
Mathematics · Medicine · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Orthopedic Surgery and Rehabilitation #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0404145

8 pages, 8 figures. Changed title and added mention of a partial result by Vassily Manturov

openalex publication_date 2004/04/07 · arxiv created 2004/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister Omega₂-moves. We also show that our proof is compatible with known results for the other move types, in the sense that every knot type admits a pair of diagrams that cannot be made identical without using all of the move types.

Cited by

• Minimal Generating sets of Reidemeister moves

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