THE BASKET NUMBERS OF KNOTS |
Bang, Je-Jun
(Gyeongju High School)
Do, Jun-Ho (Gyeongju High School) Kim, Dongseok (Department of Mathematics Kyonggi University) Kim, Tae-Hyung (Gyeongju High School) Park, Se-Han (Gyeongju High School) |
1 | D. Gabai, The Murasugi sum is a natural geometric operation II, in: Combinatorial Methods in Topology and Algebraic Geometry (Rochester, NY, USA, 1982), Amer. Math. Soc., Providence, RI, 1985, 93-100. |
2 | J. Gross, D. Robbins and T. Tucker, Genus distribution for bouquets of circles, J. Combin. Theory B. Soc. 47 (3) (1989) 292-306. DOI |
3 | J. Gross and T. Tucker, Topological graph theory, Wiley-Interscience Series in discrete Mathematics and Optimization, Wiley & Sons, New York, 1987. |
4 | J. Harer, How to construct all fibered knots and links, Topology 21 (3) (1982) 263-280. DOI ScienceOn |
5 | S. Hirose and Y. Nakashima, Seifert surfaces in open books, and pass moves on links, arXiv:1311.3383. DOI |
6 | C. Hayashi and M. Wada, Constructing links by plumbing flat annuli, J. Knot Theory Ramifications 2 (1993), 427-429. DOI |
7 | D. Kim, Basket, flat plumbing and flat plumbing basket surfaces derived from induced graphs, preprint, arXiv:1108.1455. |
8 | D. Kim, The boundaries of dipole graphs and the complete bipartite graphs , Honam. Math. J. 36 (2) (2014), 399-415, arXiv:1302.3829. DOI ScienceOn |
9 | D. Kim, A classification of links of the flat plumbing basket numbers 4 or less, Korean J. of Math. 22 (2) (2014), 253-264. DOI ScienceOn |
10 | L. H. Kauffman and S. Lambropoulou, On the Classification of Rational Knots, Adv. Appl. Math. 33 (2) (2004), 199-237. DOI ScienceOn |
11 | D. Kim, Y. S. Kwon and J. Lee, Banded surfaces, banded links, band indices and genera of links, J. Knot Theory Ramifications 22(7) 1350035 (2013), 1-18, arXiv:1105.0059. |
12 | T. Nakamura, On canonical genus of fibered knot, J. Knot Theory Ramifications 11 (2002), 341-352. DOI ScienceOn |
13 | T. Nakamura, Notes on braidzel surfaces for links, Proc. of AMS 135 (2) (2007), 559-567. DOI ScienceOn |
14 | K. Reidemeister, Homotopieringe und Linsenraume, Abh. Math. Sem. Hansischen Univ., 11 (1936), 102-109. |
15 | L. Rudolph, Quasipositive annuli (Constructions of quasipositive knots and links IV.), J. Knot Theory Ramifications 1 (4) (1992) 451-466.. DOI |
16 | L. Rudolph, Hopf plumbing, arborescent Seifert surfaces, baskets, espaliers, and homogeneous braids, Topology Appl. 116 (2001), 255-277. DOI ScienceOn |
17 | H. Schubert, Knoten mit zwei Brucken, Math. Zeitschrift, 65 (1956), 133-170. DOI |
18 | H. Seifert, Uber das Geschlecht von Knoten, Math. Ann. 110 (1934), 571-592. |
19 | 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. |
20 | M. Thistlethwaite, Knotscape, available at http://www.math.utk.edu/-morwen/knotscape. html. |
21 | T. Van Zandt. PSTricks: PostScript macros for generic TEX. Available at ftp://ftp. princeton.edu/pub/tvz/. |
22 | D. Gabai, The Murasugi sum is a natural geometric operation, in: Low-Dimensional Topology (San Francisco, CA, USA, 1981), Amer. Math. Soc., Providence, RI, 1983, 131-143. |
23 | J. H. Conway, An enumeration of knots and links and some of their algebraic properties, Proceedings of the conference on Computational problems in Abstract Algebra held at Oxford in 1967, Pergamon Press, 329-358. |
24 | Y. Choi, Y. Chung and D. Kim, The complete list of prime knots whose flat plumbing basket numbers are 6 or less, preprint, arXiv:1408.3729. |
25 | 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. DOI ScienceOn |