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Ribbon knots with different symmetric union presentations

Taizo Kanenobu and Shuhei Yoshikawa

Vol. 16 (2023), No. 1, 167–182
Abstract

We display further examples of ribbon knots with different symmetric union presentations. We show that these pairs of symmetric union diagrams are not symmetrically equivalent by the refined version of the Jones polynomial defined by Eisermann and Lamm or a certain technique introduced by Collari and Lisca.

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Keywords
ribbon knot, symmetric union presentation, symmetrically equivalence of symmetric union diagrams, refined Jones polynomial, Collari and Lisca's technique, Kauffman polynomial
Mathematical Subject Classification
Primary: 57K10, 57K14
Milestones
Received: 14 December 2021
Revised: 31 March 2022
Accepted: 31 March 2022
Published: 14 April 2023

Communicated by Kenneth S. Berenhaut
Authors
Taizo Kanenobu
Graduate School of Science
Osaka Metropolitan University
Osaka
Japan
Shuhei Yoshikawa
Department of Mathematics
Osaka City University
Osaka
Japan