Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Divide Knot Presentation of Knots of Berge's Sporadic Lens Space Surgery

  • Yamada, Yuichi (Dept. of Mathematics, The University of Electro-Communications)
  • Received : 2018.03.28
  • Accepted : 2019.06.10
  • Published : 2020.06.30
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Abstract

Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a sequel of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped curve as a divide knot. In the present paper, L-shaped curves are generalized and it is shown that every knot in the minor subfamilies, called sporadic examples of Berge's lens space surgery, is presented by a generalized L-shaped curve as a divide knot. A formula on the surgery coefficients and the presentation is also considered.

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References

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