Boundary-twisted normal form and the number of elementary moves to\n unknot

2010/10/20 by Chan-Ho Suh, Suh, Chan-Ho
Computer Science · Mathematics · #57M #57N10 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1010.4101

openalex publication_date 2010/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose K is an unknot lying in the 1-skeleton of a triangulated 3-manifold\nwith t tetrahedra. Hass and Lagarias showed there is an upper bound,\ndepending only on t, for the minimal number of elementary moves to untangle\nK. We give a simpler proof, utilizing a normal form for surfaces whose\nboundary is contained in the 1-skeleton of a triangulated 3-manifold. We also\nobtain a significantly better upper bound of 2^120t+14 and improve the\nHass--Lagarias upper bound on the number of Reidemeister moves needed to unknot\nto 2^{105 n}, where n is the crossing number.\n

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