Book Review
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MathSciNet review:
1566983
Full text of review:
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This review is available free of charge.
Book Information:
Author:
Dale Rolfsen
Title:
Knots and links
Additional book information:
Publish or Perish, Inc., Berkeley, California, 439 pp., $15.00.
J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928), no. 2, 275–306. MR 1501429, DOI 10.1090/S0002-9947-1928-1501429-1
2. J. W. Alexander, Note on Riemann spaces, Bull. Amer. Math. Soc. 26 (1920), 370-372.
Ralph H. Fox, Free differential calculus. II. The isomorphism problem of groups, Ann. of Math. (2) 59 (1954), 196–210. MR 62125, DOI 10.2307/1969686
Hugh M. Hilden, Every closed orientable $3$-manifold is a $3$-fold branched covering space of $S^{3}$, Bull. Amer. Math. Soc. 80 (1974), 1243–1244. MR 350719, DOI 10.1090/S0002-9904-1974-13699-2
Michel A. Kervaire, Les nœuds de dimensions supérieures, Bull. Soc. Math. France 93 (1965), 225–271 (French). MR 189052
Barry Mazur, On embeddings of spheres, Bull. Amer. Math. Soc. 65 (1959), 59–65. MR 117693, DOI 10.1090/S0002-9904-1959-10274-3
B. C. Mazur, On embeddings of spheres, Acta Math. 105 (1961), 1–17. MR 125570, DOI 10.1007/BF02559532
José M. Montesinos, Three-manifolds as $3$-fold branched covers of $S^{3}$, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94. MR 394630, DOI 10.1093/qmath/27.1.85
Lee Neuwirth, The algebraic determination of the genus of knots, Amer. J. Math. 82 (1960), 791–798. MR 120648, DOI 10.2307/2372940
C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. MR 90053, DOI 10.2307/1970113
H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935), no. 1, 571–592 (German). MR 1512955, DOI 10.1007/BF01448044
Arnold Shapiro and J. H. C. Whitehead, A proof and extension of Dehn’s lemma, Bull. Amer. Math. Soc. 64 (1958), 174–178. MR 103474, DOI 10.1090/S0002-9904-1958-10198-6
John Stallings, On fibering certain $3$-manifolds, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 95–100. MR 0158375
Wolfgang Haken, Theorie der Normalflächen, Acta Math. 105 (1961), 245–375 (German). MR 141106, DOI 10.1007/BF02559591
- 1.
- J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928), 275-306. MR 1501429
- 2.
- J. W. Alexander, Note on Riemann spaces, Bull. Amer. Math. Soc. 26 (1920), 370-372.
- 3.
- R. H. Fox, Free differential calculus. II, Ann. of Math. (2) 59 (1954), 196-210. MR 15, 931. MR 62125
- 4.
- H. M. Hilden, Every closed orientable 3-manifold is a 3-fold branched covering space of S, Bull. Amer. Math. Soc. 80 (1974), 1243-1244. MR 50 #3211. MR 350719
- 5.
- M. A. Kervaire, Les noeuds de dimensions supérieures, Bull. Soc. Math. France 93 (1965), 225-271. MR 32 #6479. MR 189052
- 6.
- B. Mazur, On embeddings of spheres, Bull. Amer. Math. Soc. 65 (1959), 59-65. MR 22 #8469. MR 117693
- 7.
- B. Mazur, On embeddings of spheres, Acta Math. 105 (1961), 1-17. MR 23 # A2870. MR 125570
- 8.
- J. M. Montesinos, Three manifolds as 3-fold branched covers of S, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85-94. MR 52 # 15431. MR 394630
- 9.
- L. Neuwirth, The algebraic determination of the genus of knots, Amer. J. Math. 82 (1960), 791-798. MR 22 #11397. MR 120648
- 10.
- C. D. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1-26. MR 19, 761. MR 90053
- 11.
- H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1934), 571-592. MR 1512955
- 12.
- A. Shapiro and J. H. C. Whitehead, A proof and extension of Dehn's lemma, Bull. Amer. Math. Soc. 64 (1958), 174-178. MR 21 #2242. MR 103474
- 13.
- J. R. Stallings, On fibering certain 3-manifolds, Topology of 3-manifolds and related topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 95-100. MR 28 # 1600. MR 158375
- 14.
- W. Haken, Theorie der Normalflächen, Acta Math. 105 (1961), 245-375. MR 25 #4519a. MR 141106
Review Information:
Reviewer:
Lee P. Neuwirth
Journal:
Bull. Amer. Math. Soc.
83 (1977), 931-935
DOI:
https://doi.org/10.1090/S0002-9904-1977-14327-9