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arXiv · 2002.11292

Cocycles of $G$-Alexander biquandles and $G$-Alexander multiple conjugation biquandles

Atsushi Ishii·Masahide Iwakiri·Seiichi Kamada·Jieon Kim·Shosaku Matsuzaki·Kanako Oshiro
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Abstract

Biquandles and multiple conjugation biquandles are algebras which are related to links and handlebody-links in $3$-space. Cocycles of them can be used to construct state-sum type invariants of links and handlebody-links. In this paper we discuss cocycles of a certain class of biquandles and multiple conjugation biquandles, which we call $G$-Alexander biquandles and $G$-Alexander multiple conjugation biquandles, with a relationship with group cocycles. We give a method to obtain a (biquandle or multiple conjugation biquandle) cocycle of them from a group cocycle.

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Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro. 2020-02-26. Cocycles of $G$-Alexander biquandles and $G$-Alexander multiple conjugation biquandles. https://arxiv.org/abs/2002.11292

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