Ribbon knots with different symmetric union presentations

Kanenobu, Taizo; Yoshikawa, Shuhei

doi:10.2140/involve.2023.16.167

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Ribbon knots with different symmetric union presentations

Taizo Kanenobu and Shuhei Yoshikawa

Vol. 16 (2023), No. 1, 167–182

DOI: 10.2140/involve.2023.16.167

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.

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

Vol. 16, No. 1, 2023