On generating sets of Yoshikawa moves for marked graph diagrams of surface-links-Reference-Cited by-同舟云学术

On generating sets of Yoshikawa moves for marked graph diagrams of surface-links

Published:2015-04 Issue:04 Volume:24 Page:1550018
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Kim Jieon¹,Joung Yewon¹,Lee Sang Youl²

Affiliation:

1. Department of Mathematics, Graduate School of Natural Sciences, Pusan National University, Busan 609-735, Republic of Korea

2. Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea

Abstract

A marked graph diagram is a link diagram possibly with marked 4-valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked graph diagrams. Specially, K. Yoshikawa suggested local moves on marked graph diagrams, nowadays called Yoshikawa moves. It is now known that two marked graph diagrams representing equivalent surface-links are related by a finite sequence of these Yoshikawa moves. In this paper, we provide some generating sets of Yoshikawa moves on marked graph diagrams representing unoriented surface-links, and also oriented surface-links. We also discuss independence of certain Yoshikawa moves from the other moves.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216515500182

Reference23 articles.

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4. IDEAL COSET INVARIANTS FOR SURFACE-LINKS IN ℝ4

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