Hiroshima Mathematical Journal

A multiple conjugation biquandle and handlebody-links

Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, and Kanako Oshiro

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Abstract

We introduce a multiple conjugation biquandle, and show that it is the universal algebra for defining a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of $n$-parallel biquandle operations for any integer $n$, and show that any biquandle gives a multiple conjugation biquandle with them.

Article information

Source
Hiroshima Math. J., Volume 48, Number 1 (2018), 89-117.

Dates
Received: 11 February 2017
Revised: 12 September 2017
First available in Project Euclid: 8 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1520478026

Digital Object Identifier
doi:10.32917/hmj/1520478026

Mathematical Reviews number (MathSciNet)
MR3772003

Zentralblatt MATH identifier
06901790

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
biquandles multiple conjugation biquandles handlebody-links parallel biquandle operations quandles

Citation

Ishii, Atsushi; Iwakiri, Masahide; Kamada, Seiichi; Kim, Jieon; Matsuzaki, Shosaku; Oshiro, Kanako. A multiple conjugation biquandle and handlebody-links. Hiroshima Math. J. 48 (2018), no. 1, 89--117. doi:10.32917/hmj/1520478026. https://projecteuclid.org/euclid.hmj/1520478026


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