SYMMETRIC QUANDLE COLORINGS FOR SPATIAL GRAPHS AND HANDLEBODY-LINKS-Reference-Cited by-同舟云学术

SYMMETRIC QUANDLE COLORINGS FOR SPATIAL GRAPHS AND HANDLEBODY-LINKS

Published:2012-04 Issue:04 Volume:21 Page:1250050
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

JANG YEONHEE¹,OSHIRO KANAKO²

Affiliation:

1. Department of Mathematics, Hiroshima University, Higashi-hiroshima 739-8526, Japan

2. Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women's University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo 112-8681, Japan

Abstract

In this paper, colorings by symmetric quandles for spatial graphs and handlebody-links are introduced. We also introduce colorings by LH-quandles for LH-links. LH-links are handlebody-links, some of whose circle components are specified, which are related to Heegaard splittings of link exteriors. We also discuss quandle (co)homology groups and cocycle invariants.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216511010024

Reference15 articles.

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

2. Symmetric extensions of dihedral quandles and triple points of non-orientable surfaces

3. RACKS AND LINKS IN CODIMENSION TWO

4. Moves and invariants for knotted handlebodies

5. CALCULATION OF DIHEDRAL QUANDLE COCYCLE INVARIANTS OF TWIST SPUN 2-BRIDGE KNOTS

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Handlebody-knots and development of quandle theory;Sugaku Expositions;2022-04-07

2. Surface-Knots in 4-Space;Springer Monographs in Mathematics;2017

3. The Markov theorems for spatial graphs and handlebody-knots with Y-orientations;International Journal of Mathematics;2015-12

4. Qualgebras and knotted 3-valent graphs;Fundamenta Mathematicae;2015

5. A $G$-family of quandles and handlebody-knots;Illinois Journal of Mathematics;2013-01-01