Divide knot presentation of sporadic knots of Berge's lens space surgery

Yuichi Yamada

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arXiv · 1210.2905

Divide knot presentation of sporadic knots of Berge's lens space surgery

Yuichi Yamada

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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 continuation 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 generalized.

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BibTeX RIS

Yuichi Yamada. 2012-10-10. Divide knot presentation of sporadic knots of Berge's lens space surgery. https://arxiv.org/abs/1210.2905

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