An algorithm to classify rational 3-tangles

2014/06/17 by Bo-hyun Kwon, Kwon, Bo-hyun · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1406.4496

openalex publication_date 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A 3-tangle T is the disjoint union of 3 properly embedded arcs in the unit 3-ball; it is called rational if there is a homeomorphism of pairs from (B³,T) to (D²× I,\x₁,x₂,x₃\× I). Two rational 3-tangles T and T' are isotopic if there is an orientation-preserving self-homeomorphism h: (B³, T)→ (B³,T') that is the identity map on the boundary. In this paper, we give an algorithm to check whether or not two rational 3-tangles are isotopic by using a modified version of Dehn's method for classifying simple closed curves on surfaces.

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• A classification of rational 3-tangles

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