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Cubes with knotted holes. (English) Zbl 0213.25005


MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
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References:

[1] J. W. Alexander and G. B. Briggs, On types of knotted curves, Ann. of Math. (2) 28 (1926/27), no. 1-4, 562 – 586. · JFM 53.0549.02
[2] R. H. Bing, Necessary and sufficient conditions that a 3-manifold be \?³, Ann. of Math. (2) 68 (1958), 17 – 37. · Zbl 0081.39202
[3] R. H. Bing, Correction to ”Necessary and sufficient conditions that a 3-manifold be \?³”, Ann. of Math. (2) 77 (1963), 210. · Zbl 0115.17304
[4] -, Some aspects of the topology of \( 3\)-manifolds related to the Poincaré conjecture, Lectures on Modern Math., vol. 2, Wiley, New York, 1964, pp. 93-128. MR 30 #2474.
[5] -, Computing the fundamental group of the complement of curves, Washington State University, Pullman, Wash., 1965.
[6] Garrett Birkhoff and Saunders Mac Lane, A survey of modern algebra, Third edition, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1965. · Zbl 0061.04802
[7] A. C. Conner, Splittable knots (preprint).
[8] H. S. M. Coxeter, The abstract groups \?^{\?,\?,\?}, Trans. Amer. Math. Soc. 45 (1939), no. 1, 73 – 150. · Zbl 0020.20703
[9] H. S. M. Coxeter, The abstract group \?^{3,7,16}, Proc. Edinburgh Math. Soc. (2) 13 (1962), 47 – 61. · Zbl 0118.03702
[10] 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
[11] H. Gluck, Ph.D. Thesis, Princeton University, Princeton, N. J., 1961.
[12] John Hempel, Construction of orientable 3-manifolds, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 207 – 212. · Zbl 1246.57043
[13] John Hempel, A simply connected 3-manifold is \?³ if it is the sum of a solid torus and the complement of a torus knot, Proc. Amer. Math. Soc. 15 (1964), 154 – 158. · Zbl 0118.18802
[14] W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math. (2) 76 (1962), 531 – 540. · Zbl 0106.37102
[15] Lee Neuwirth, The algebraic determination of the genus of knots, Amer. J. Math. 82 (1960), 791 – 798. · Zbl 0117.41001
[16] Dieter Noga, Über den Aussenraum von Produktknoten und die Bedeutung der Fixgruppen, Math. Z. 101 (1967), 131 – 141 (German). · Zbl 0183.52102
[17] C. D. Papakyriakopoulos, On solid tori, Proc. London Math. Soc. (3) 7 (1957), 281 – 299. · Zbl 0078.16305
[18] C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1 – 26. · Zbl 0078.16402
[19] H. Poincaré, Second complément a l’analysis situs, Proc. London Math. Soc. (2) 32 (1900), 277-308. · JFM 31.0477.10
[20] -, Cinquieme complément a l’analysis situs, Rend. Circ. Mat. Palermo 18 (1904), 45-110. · JFM 35.0504.13
[21] H. F. Trotter, Non-invertible knots exist, Topology 2 (1963), 275 – 280. · Zbl 0136.21203
[22] Andrew H. Wallace, Modifications and cobounding manifolds, Canad. J. Math. 12 (1960), 503 – 528. · Zbl 0108.36101
[23] J. H. C. Whitehead, On doubled knots, J. London Math. Soc. 12 (1937), 63-71. · Zbl 0016.04402
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