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

被引：3

作者：

Kamada, Seiichi ^{[1
]}

Kawauchi, Akio ^{[2
]}

Kim, Jieon ^{[3
]}

Lee, Sang Youl ^{[3
]}

机构：

[1] Osaka City Univ, Dept Math, Sumiyoshi Ku, Osaka 5588585, Japan

[2] Osaka City Univ, Adv Math Inst, Sumiyoshi Ku, Osaka 5588585, Japan

[3] Pusan Natl Univ, Dept Math, Busan 46241, South Korea

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2018年 / 27卷 / 11期

基金：

新加坡国家研究基金会;

关键词：

Link; surface-link; marked graph diagram; biquandle cocycle invariant; shadow biquandle cocycle invariant; MARKED GRAPH DIAGRAMS; GENERATING SETS; HOMOLOGY; QUANDLE; 4-SPACE; KNOTS; MOVES;

D O I：

10.1142/S0218216518430162

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：37

共 24 条

[1] [Anonymous], 1998, Banach Center Publications
[2] [Anonymous], 1998, Mathematical Surveys and Monographs
[3] CALCULATING THE FUNDAMENTAL BIQUANDLES OF SURFACE LINKS FROM THEIR CH-DIAGRAMS
Ashihara, Sosuke
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2012, 21 (10)
[4] Carrell T., 2009, The surface biquandle
[5] Quandle cohomology and state-sum invariants of knotted curves and surfaces
Carter, JS
Jelsovsky, D
Kamada, S
Langford, L
Saito, M
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (10) : 3947 - 3989
[6] Homology theory for the set-theoretic Yang-Baxter equation and knot invariants from generalizations of quandles
Carter, JS
Elhamdadi, M
Saito, M
[J]. FUNDAMENTA MATHEMATICAE, 2004, 184 : 31 - 54
[7] Geometric interpretations of quandle homology
Carter, JS
Kamada, S
Saito, M
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2001, 10 (03) : 345 - 386
[8] Trunks and classifying spaces
Fenn, R
Rourke, C
Sanderson, B
[J]. APPLIED CATEGORICAL STRUCTURES, 1995, 3 (04) : 321 - 356
[9] Fenn R., 1992, Journal of Knot Theory and Its Ramifications, V1, P343
[10] A CLASSIFYING INVARIANT OF KNOTS, THE KNOT QUANDLE
JOYCE, D
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1982, 23 (01) : 37 - 65

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