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On a certain numerical invariant of link types. (English) Zbl 0137.17903


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topology
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[1] Kunio Murasugi, On the genus of the alternating knot. I, II, J. Math. Soc. Japan 10 (1958), 94 – 105, 235 – 248. , https://doi.org/10.2969/jmsj/01010094 Richard Crowell, Genus of alternating link types, Ann. of Math. (2) 69 (1959), 258 – 275. · Zbl 0111.35803
[2] Ralph H. Fox, On the imbedding of polyhedra in 3-space, Ann. of Math. (2) 49 (1948), 462 – 470. · Zbl 0032.12502
[3] -, Free differential calculus. I, Ann. of Math. (2) 57 (1953), 547-560; II, ibid. 59 (1954), 196-210; III, ibid. 64 (1956), 407-419.
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[5] R. H. Fox, Some problems in knot theory, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 168 – 176. · Zbl 1246.57011
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[9] Burton W. Jones, The Arithmetic Theory of Quadratic Forms, Carcus Monograph Series, no. 10, The Mathematical Association of America, Buffalo, N. Y., 1950.
[10] Shin\(^{\prime}\)ichi Kinoshita, On Wendt’s theorem of knots, Osaka Math. J. 9 (1957), 61 – 66. · Zbl 0080.16903
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[12] Kunio Murasugi, On the genus of the alternating knot. I, II, J. Math. Soc. Japan 10 (1958), 94 – 105, 235 – 248. , https://doi.org/10.2969/jmsj/01010094 Richard Crowell, Genus of alternating link types, Ann. of Math. (2) 69 (1959), 258 – 275. · Zbl 0111.35803
[13] Kunio Murasugi, On alternating knots, Osaka Math. J. 12 (1960), 277 – 303. · Zbl 0113.38603
[14] Kunio Murasugi, On the definition of the knot matrix, Proc. Japan Acad. 37 (1961), 220 – 221. · Zbl 0113.38604
[15] Kunio Murasugi, Non-amphicheirality of the special alternating links, Proc. Amer. Math. Soc. 13 (1962), 771 – 776. · Zbl 0138.19005
[16] K. Reidemeister, Knotentheorie, Chelsea, New York, 1948. · JFM 58.1202.04
[17] Horst Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1949 (1949), no. 3, 57 – 104 (German). · Zbl 0031.28602
[18] H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935), no. 1, 571 – 592 (German). · Zbl 0010.13303
[19] -, Die Verschlingungsinvarianten der zyklischen Knotenüberlagerungen, Abh. Math. Sem. Univ. Hamburg 11 (1935), 84-101. · Zbl 0011.17802
[20] Hidetaka Terasaka, On null-equivalent knots, Osaka Math. J. 11 (1959), 95 – 113. · Zbl 0106.16703
[21] Guillermo Torres, On the Alexander polynomial, Ann. of Math. (2) 57 (1953), 57 – 89. · Zbl 0050.17903
[22] H. F. Trotter, Homology of group systems with applications to knot theory, Ann. of Math. (2) 76 (1962), 464 – 498. · Zbl 0108.18302
[23] H. Wendt, Die gordische Auflösung von Knoten, Math. Z. 42 (1937), no. 1, 680 – 696 (German). · Zbl 0016.42005
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