Korean J. Math.  Vol 22, No 2 (2014)  pp.253-264
DOI: https://doi.org/10.11568/kjm.2014.22.2.253

A classification of links of the flat plumbing basket numbers $4$ or less

Dongseok Kim


Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers $4$ or less using a special presentation of the flat plumbing basket surfaces. We find a complete classification theorem of links of the flat plumbing basket numbers $4$ or less.


Links, Seifert surfaces, Flat plumbing basket number

Subject classification

57M27; 57M25; 57R56


This work was supported by Kyonggi University Research Grant 2011.

Full Text:



Y. Choi, Y. Do and D. Kim, A new classification of links by the flat plumbing basket numbers, preprint. (Google Scholar)

R. Furihata, M. Hirasawa and T. Kobayashi, Seifert surfaces in open books, and a new coding algorithm for links, Bull. London Math. Soc. 40(3) (2008), 405–414. (Google Scholar)

D. Gabai, Genera of the arborescent links, Mem. Amer. Math. Soc. 59 (339) (1986) I.VIII, 1–98. (Google Scholar)

S. Hirose and Y. Nakashima, Seifert surfaces in open books, and pass moves on links, arXiv:1311.3383. (Google Scholar)

D. Kim, Basket, flat plumbing and flat plumbing basket surfaces derived from induced graphs, preprint, arXiv:1108.1455. (Google Scholar)

D. Kim, Y. S. Kwon and J. Lee, Banded surfaces, banded links, band indices and genera of links, J. Knot Theory Ramifications, arXiv:1105.0059. (Google Scholar)

L. Rudolph, Hopf plumbing, arborescent Seifert surfaces, baskets, espaliers, and homogeneous braids, Topology Appl. 116 (2001), 255–277. (Google Scholar)

H. Seifert, Uber das Geschlecht von Knoten, Math. Ann. 110 (1934), 571–592. (Google Scholar)

J. Stallings, Constructions of fibred knots and links, in: Algebraic and Geometric Topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, CA, 1976), Part 2, Amer. Math. Soc., Providence, RI, 1978, pp. 55–60. (Google Scholar)

T. Van Zandt. PSTricks: PostScript macros for generic TEX. Available at ftp://ftp. princeton.edu/pub/tvz/. (Google Scholar)


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