Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle

2007/11/15 by Joel Hass, Hass, Joel, Tahl Nowik +1
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0711.2350

openalex publication_date 2007/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a sequence of diagrams of the unknot for which the minimum number of Reidemeister moves required to pass to the trivial diagram is quadratic with respect to the number of crossings. These bounds apply both in S² and in \R².

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