Equivalence of rational links and 2-bridge links revisited

2014/06/11 by Margarita Toro, Margarita M. Toro, Toro, Margarita M.
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1406.2955

14 pages, 7 figures

arxiv created 2014/06/11 · openalex publication_date 2014/06/11 · arxiv updated 2014/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a simple proof of the equivalence between the rational link associated to the continued fraction [ a₁,a₂,⋯ a_m], a_i∈ℕ, and the two bridge link of type p/q, where p/q is the rational given by [ a₁%,a₂,⋯ a_m] . The known proof of this equivalence relies on the two fold cover of a link and the classification of the lens spaces. Our proof is elementary and combinatorial and follows the naive approach of finding a set of movements to transform the rational link given by [ a₁,a₂,⋯ a_m] into the two bridge link of type p/q.

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