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On the problems of determining knots by their complements and knot complements by their groups. (English) Zbl 0329.55002


MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
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References:

[1] R. H. Bing and J. M. Martin, Cubes with knotted holes, Trans. Amer. Math. Soc. 155 (1971), 217 – 231. , https://doi.org/10.1090/S0002-9947-1971-0278287-4 Jonathan Simon, Some classes of knots with property \?, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969), Markham, Chicago, Ill., 1970, pp. 195 – 199.
[2] Gerhard Burde and Heiner Zieschang, Eine Kennzeichnung der Torusknoten, Math. Ann. 167 (1966), 169 – 176 (German). · Zbl 0145.20502 · doi:10.1007/BF01362170
[3] A. Connor, Splittable knots, Ph.D. Thesis, Univ. of Georgia, Athens, Ga., 1969.
[4] Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Based upon lectures given at Haverford College under the Philips Lecture Program, Ginn and Co., Boston, Mass., 1963. · Zbl 0362.55001
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[9] J. P. Neuzil, Surgery on a curve in a solid torus, Trans. Amer. Math. Soc. 204 (1975), 385 – 406. · Zbl 0306.55003
[10] Dieter Noga, Über den Aussenraum von Produktknoten und die Bedeutung der Fixgruppen, Math. Z. 101 (1967), 131 – 141 (German). · Zbl 0183.52102 · doi:10.1007/BF01136030
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[12] Jonathan Simon, An algebraic classification of knots in \?³, Ann. of Math. (2) 97 (1973), 1 – 13. · Zbl 0256.55003 · doi:10.2307/1970874
[13] Jonathan Simon, On knots with nontrivial interpolating manifolds, Trans. Amer. Math. Soc. 160 (1971), 467 – 473. · Zbl 0232.55005
[14] -, Some classes of knots with property \( P\), Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969), Markham, Chicago, Ill., 1970, pp. 195-199. MR 43 #4018b.
[15] F. Waldhausen, On the determination of some bounded \( 3\)-manifolds by their fundamental groups alone, Proc. Internat. Sympos. Topology and Appl. (Herzog-Novi, Yugoslavia, 1968), Beograd, 1969, pp. 331-332.
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