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Kyungpook Mathematical Journal 2020; 60(2): 255-277

Published online June 30, 2020

Copyright © Kyungpook Mathematical Journal.

Divide Knot Presentation of Knots of Berge's Sporadic Lens Space Surgery

Yuichi Yamada

Dept. of Mathematics, The University of Electro-Communications, 1-5-1, Chofu- gaoka, Chofu, Tokyo, 182-8585, Japan
e-mail : yyyamada@e-one.uec.ac.jp

Received: March 28, 2018; Revised: June 7, 2019; Accepted: June 10, 2019

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.

Keywords: Dehn surgery, lens space, plane curve