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Edges of Canonical Decompositions for 2-Bridge Knots and Links

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Abstract

Let L=C(a1,..., ak) be a hyperbolic 2-bridge knot or link. We give a family of arcs in S3−L which are ambient isotopic to edges of the canonical decomposition of S3−L if each ∣aj∣ is sufficiently large. This result supports the conjecture that the decomposition of S3−L given by Sakuma–Weeks in [12] is the canonical one.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, 33, Fukuoka, 812-81, Japan

    Hirotaka Akiyoshi

  2. Department of Electrical Engineering and Computer Science, Osaka Prefectural College of Technology, Saiwai-cho 26-12, Neyagawa Osaka, 572, Japan

    Han Yoshida

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  1. Hirotaka Akiyoshi
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  2. Han Yoshida
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Akiyoshi, H., Yoshida, H. Edges of Canonical Decompositions for 2-Bridge Knots and Links. Geometriae Dedicata 74, 291–304 (1999). https://doi.org/10.1023/A:1005043904681

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