Research ArticleNo Access

Quandle coloring quivers of surface-links

Jieon Kim

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

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Avenue, Claremont, 91711, CA, US

E-mail Address: jieonkim7@gmail.com

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Sam Nelson

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

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Avenue, Claremont, 91711, CA, US

E-mail Address: Sam.Nelson@cmc.edu

Corresponding author.

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Minju Seo

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

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Avenue, Claremont, 91711, CA, US

E-mail Address: mingzuu@pusan.ac.kr

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https://doi.org/10.1142/S0218216521500024Cited by:0 (Source: Crossref)

Abstract

Quandle coloring quivers are directed graph-valued invariants of oriented knots and links, defined using a choice of finite quandle $X$ and set $S \subset Hom (X, X)$ of endomorphisms. From a quandle coloring quiver, a polynomial knot invariant known as the in-degree quiver polynomial is defined. We consider quandle coloring quiver invariants for oriented surface-links, represented by marked graph diagrams. We provide example computations for all oriented surface-links with ch-index up to 10 for choices of quandles and endomorphisms.

Keywords:

AMSC: 57K12

References

1. K. Cho and S. Nelson, Quandle coloring quivers, J. Knot Theory Ramifications 28(1) (2019) 1950001. Link, Web of Science, Google Scholar
2. M. Elhamdadi and S. Nelson, Quandles: An Introduction to the Algebra of Knots, Student Mathematical Library, Vol. 74 (American Mathematical Society, Providence, RI, 2015). Crossref, Google Scholar
3. J. Kim, Y. Joung and S. Y. Lee, On the Alexander biquandles of oriented surface-links via marked graph diagrams, J. Knot Theory Ramifications, 23(7) (2014) 1460007. Link, Web of Science, Google Scholar
4. J. Kim, Y. Joung and S. Y. Lee, On generating sets of Yoshikawa moves for marked graph diagrams of surface-links, J. Knot Theory Ramifications 24(4) (2015) 1550018. Link, Web of Science, Google Scholar
5. S. J. Lomonaco, Jr, The homotopy groups of knots: I how to compute the algebraic $2$ -type, Pacific J. Math. 95(2) (1981) 349–390. Crossref, Web of Science, Google Scholar
6. S. Nelson and W. D. Neumann, The 2-generalized knot group determines the knot, Commun. Contemp. Math. 10(1) (2008) 843–847. Link, Google Scholar