Biquandle cohomology and state-sum invariants of links and surface-links-Reference-Cited by-同舟云学术

Biquandle cohomology and state-sum invariants of links and surface-links

Published:2018-10 Issue:11 Volume:27 Page:1843016
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Kamada Seiichi¹,Kawauchi Akio²,Kim Jieon³,Lee Sang Youl³

Affiliation:

1. Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

2. Osaka City University Advanced Mathematical Institute, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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

Abstract

In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute the biquandle cocycle invariants from marked graph diagrams. We also develop the shadow (co)homology theory of biquandles and construct the shadow biquandle cocycle invariants for oriented surface-links.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216518430162

Reference22 articles.

1. CALCULATING THE FUNDAMENTAL BIQUANDLES OF SURFACE LINKS FROM THEIR CH–DIAGRAMS

2. Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles

3. Quandle cohomology and state-sum invariants of knotted curves and surfaces

4. GEOMETRIC INTERPRETATIONS OF QUANDLE HOMOLOGY

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