Korean Journal of Mathematics

  • 제22권2호
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  • Pages.253-264
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  • 2014
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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A CLASSIFICATION OF LINKS OF THE FLAT PLUMBING BASKET NUMBERS 4 OR LESS

  • 투고 : 2014.03.19
  • 심사 : 2014.05.19
  • 발행 : 2014.06.30
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초록

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.

키워드

참고문헌

  1. Y. Choi, Y. Do and D. Kim, A new classification of links by the flat plumbing basket numbers, preprint.
  2. 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. https://doi.org/10.1112/blms/bdn020
  3. D. Gabai, Genera of the arborescent links, Mem. Amer. Math. Soc., 59 (339)(1986) I.VIII, 1-98.
  4. S. Hirose and Y. Nakashima, Seifert surfaces in open books, and pass moves on links, arXiv:1311.3383.
  5. D. Kim, Basket, flat plumbing and flat plumbing basket surfaces derived from induced graphs, preprint, arXiv:1108.1455.
  6. D. Kim, Y. S. Kwon and J. Lee, Banded surfaces, banded links, band indices and genera of links, J. Knot Theory Ramifications ,22 (7) (2013), 1350035,1-18, arXiv:1105.0059.
  7. L. Rudolph, Hopf plumbing, arborescent Seifert surfaces, baskets, espaliers, and homogeneous braids, Topology Appl. 116 (2001), 255-277. https://doi.org/10.1016/S0166-8641(00)90091-9
  8. H. Seifert, Uber das Geschlecht von Knoten, Math. Ann. 110 (1934), 571-592.
  9. J. Stallings, Constructions of fibred knots and links, in: Algebraic and Geometric Topology (Proc. Sympos. PureMath., Stanford Univ., Stanford, CA, 1976), Part 2, Amer. Math. Soc., Providence, RI, 1978, pp. 55-60.
  10. T. Van Zandt. PSTricks: PostScript macros for generic TEX. Available at ftp://ftp.princeton.edu/pub/tvz/.

피인용 문헌

  1. THE BASKET NUMBERS OF KNOTS vol.23, pp.1, 2014, https://doi.org/10.11568/kjm.2015.23.1.115
  2. The complete list of prime knots whose flat plumbing basket numbers are 6 or less vol.24, pp.7, 2014, https://doi.org/10.1142/s021821651550042x