Biquandle (co)homology and handlebody-links-Reference-Cited by-同舟云学术

Biquandle (co)homology and handlebody-links

Published:2018-10 Issue:11 Volume:27 Page:1843011
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Ishii Atsushi¹,Iwakiri Masahide²,Kamada Seiichi³,Kim Jieon⁴,Matsuzaki Shosaku⁵,Oshiro Kanako⁶

Affiliation:

1. Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan

2. Graduate School of Science and Engineering, Saga University, Saga 840-8502, Japan

3. Department of Mathematics, Osaka City University, Osaka 558-8585, Japan

4. Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

5. Faculty of Engineering, Takushoku University, Tokyo 193-0985, Japan

6. Department of Information and Communication Sciences, Sophia University, Tokyo 102-8554, Japan

Abstract

In this paper, we introduce the (co)homology group of a multiple conjugation biquandle. It is the (co)homology group of the prismatic chain complex, which is related to the homology of foams introduced by J. S. Carter, modulo a certain subchain complex. We construct invariants for [Formula: see text]-oriented handlebody-links using [Formula: see text]-cocycles. When a multiple conjugation biquandle [Formula: see text] is obtained from a biquandle [Formula: see text] using [Formula: see text]-parallel operations, we provide a [Formula: see text]-cocycle (or [Formula: see text]-cocycle) of the multiple conjugation biquandle [Formula: see text] from a [Formula: see text]-cocycle (or [Formula: see text]-cocycle) of the biquandle [Formula: see text] equipped with an [Formula: see text]-set [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216518430113

Reference15 articles.

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