×

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


Keywords:

topology
Full Text: DOI

References:

[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 · doi:10.2307/1970181
[2] Ralph H. Fox, On the imbedding of polyhedra in 3-space, Ann. of Math. (2) 49 (1948), 462 – 470. · Zbl 0032.12502 · doi:10.2307/1969291
[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.
[4] R. H. Fox, A quick trip through knot theory, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 120 – 167. · Zbl 1246.57002
[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
[6] G. Torres and R. H. Fox, Dual presentations of the group of a knot, Ann. of Math. (2) 59 (1954), 211 – 218. · Zbl 0055.16805 · doi:10.2307/1969687
[7] Lebrecht Goeritz, Knoten und quadratische Formen, Math. Z. 36 (1933), no. 1, 647 – 654 (German). · Zbl 0006.42201 · doi:10.1007/BF01188642
[8] Yoko Hashizume, On the uniqueness of the decomposition of a link, Osaka Math. J. 10 (1958), 283 – 300. · Zbl 0106.16704
[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
[11] R. H. Kyle, Branched covering spaces and the quadratic forms of links, Ann. of Math. (2) 59 (1954), 539 – 548. · Zbl 0055.42103 · doi:10.2307/1969717
[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 · doi:10.2307/1970181
[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 · doi:10.1007/BF01448044
[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 · doi:10.2307/1969726
[22] H. F. Trotter, Homology of group systems with applications to knot theory, Ann. of Math. (2) 76 (1962), 464 – 498. · Zbl 0108.18302 · doi:10.2307/1970369
[23] H. Wendt, Die gordische Auflösung von Knoten, Math. Z. 42 (1937), no. 1, 680 – 696 (German). · Zbl 0016.42005 · doi:10.1007/BF01160103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.