Available in electronic format
Available in print format		 Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues: 1891 - Present
Previous Article
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF DVI PostScript

Book Information

Author(s): G. Burde and H. Zieschang
Title: Knots
Additional book information: de Gruyter Stud. Math., vol. 5, Walter de Gruyter, New York, 2003, xii+559, $69.95, 3-11-017005-1

Author(s): Jonathan Hillman
Title: Algebraic invariants of links
Additional book information: Series on Knots and Everything, Volume 32, World Scientific Co. Pte. Ltd., Singapore, 2002, xii+305, $42.00, 789812-381545

References:

[A20]
J.W. Alexander, Note on Riemann spaces, Bull. Amer. Math. Soc. 26 (1920), 370-372.

[A25]
E. Artin, Zur Isotopie zweidimensionaler Flächen in $\mathbb R^4$, Abh. Math. Sem. Univ. Hamburg 4 (1925), 174-177.

[A88]
M.F. Atiyah, New invariants of $3$ and $4$dimensional manifolds, Sympos. on the Math. Heritage of Hermann Weyl (R.O. Wells, ed.), 1987, Amer. Math. Soc., Providence, RI, 1988, 285-299. MR 89m:57034

[CS98]
J.S. Carter and M. Saito, Knotted Surfaces and Their Diagrams, Mathematical Surveys and Monographs 55, Amer. Math. Soc., Providence, RI, 1998. MR 98m:57027

[CG75]
A. Casson and C. McA. Gordon, Cobordism of classical knots, in A la Recherche de la Topologie Perdue (Guillou and Marin, eds.), Progr. Math. 62, 1986, 181-199; originally published as Orsay Preprint, 1975. MR 88k:57002

[C90]
T.D. Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Memoirs of the Amer. Math. Soc. 84, Amer. Math. Soc., Providence, RI, 1990. MR 91c:57005

[COT03]
T.D. Cochran, K.E. Orr and P. Teichner, Knot concordance, Whitney towers and $L^2$-signatures, Annals of Math. 157 (2003), 433-519.

[E99]
M. Epple, Geometric aspects in the development of knot theory, in History of Topology (I.M. James, ed.), North-Holland, Amsterdam, 1999, 301-358. MR 2000i:57001

[F75]
M. Farber, Linking coefficients and two-dimensional knots, Soviet Math. Dokl. 16 (1975), 647-650. MR 53:4081

[FM66]
R.H. Fox and J.W. Milnor, Singularities of $2$-spheres in $4$-space and cobordism of knots, Osaka Math. J. 3 (1960), 257-267. MR 35:2273

[G33]
C.F. Gauss, Werke, 6 Volumes, Königliche Gesellschaft der Wissenschaften, Göttingen, 1863-1933, Vol. VI, 106-118.

[G76]
C.H. Giffen, F-isotopy and I-equivalence, unpublished manuscript, Univ. of Virginia, 1976.

[G83]
P.M. Gilmer, Slice knots in $S^3$, Quart. J. Math. 34 (1983), 305-322. MR 85d:57004

[G93]
P.M. Gilmer, Classical knot and link concordance, Comment. Math. Helv. 69 (1993), 1-19. MR 94c:57007

[G79]
C. McA. Gordon, Some aspects of classical knot theory, in Knot Theory, Proceedings, Plans-sur-Bex, Switzerland 1977 (J.C. Haussmann, ed.), Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1979, 1-60. MR 80f:57002

[G72]
M. Gutierrez, On knot modules, Invent. Math. 17 (972), 329-335. MR 47:9636

[HL90]
N. Habegger and X.S. Lin, The classification of links up to link-homotopy, J. Amer. Math. Soc. 3 (1990), 389-419. MR 91e:57015

[H61]
W. Haken, Theorie der Normalflächen, Acta Mathematica 105 (1961), 245-375. MR 25:4519a

[H93]
J. Hughes, Structured groups and link-homotopy, J. Knot Theory and its Ramifications 2 (1993), 37-63. MR 94c:57008

[H98]
J. Hughes, Distinguishing link-homotopy classes by pre-peripheral structures, J. Knot Theory and its Ramifications 7 (1998), 925-944. MR 2000f:57007

[K87]
L.H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407. MR 88f:57006

[K64]
M. Kervaire, Les noeuds de dimension supérieure, Bull. Soc. Math. de France 93 1965, 225-271. MR 32:6479

[K65]
M. Kervaire, On higher-dimensional knots, in Differential and Combinatorial Topology (S. Cairn, ed.), Princeton Univ. Press, 1965, 105-120. MR 31:2732

[KW79]
M. Kervaire and C. Weber, A survey of multidimensional knots, in Knot Theory, Proceedings, Plans-sur-Bex, Switzerland 1977 (J.C. Haussmann, ed.), Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1979, 61-134. MR 80f:57009

[K97]
R. Kirby, Problems in low-dimensional topology (R. Kirby, ed.), AMS/IP Stud. Adv. Math., 2.2, Geometric topology, Athens, GA, 1993, 33-473, Amer. Math. Soc., Providence, RI, 1997.

[KL99]
P. Kirk and C. Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants, Topology 38 (1999), 635-661. MR 2000c:57010

[K11]
C.G. Knott, Life and Scientific Work of Peter Guthrie Tait, Cambridge Univ. Press, Cambridge, 1911.

[L00]
C. Letsche, A new slicing obstruction using the eta invariant, Proc. Cambridge Philos. Soc. 128 (2000), 301-319. MR 2001b:57017

[L69]
J. Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969), 229-244. MR 39:7618

[L77]
J. Levine, Knot modules: I, Trans. Amer. Math. Soc. 229 (1977), 1-50. MR 57:1503

[L88]
J. Levine, An approach to homotopy classification of links, Trans. Amer. Math. Soc. 306 (1988), 361-387. MR 88m:57008

[LO03]
J. Levine and K. Orr, A survey of applicatioons of surgery to knot and link theory, in Surveys on Surgery Theory, Vol. 1 (S. Cappell, A. Ranicki, J. Rosenberg, eds.), Ann. of Math. Studies 145, Princeton, NJ, 2003, 345-364. MR 2001e:57034

[L48]
J.B. Listing, Vorstudien zur Topologie, Göttingen Studien 2 (1848), 811-875; separately published: Vandenhoeck und Ruprecht, Göttingen, 1848.

[L03]
C. Livingston, A survey of classical knot concordance, preprint, arXiv:math.GT/0307077, 2003.

[M91]
J.C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., Clarendon Press, Oxford, 1891; reprinted by Dover Publications, NY, 1954. MR 16:99b

[MT93]
W. Menasco and M.B. Thistlethwaite, The classification of alternating links, Annals of Math. 138 (1993), 113-171. MR 95g:57015

[M54]
J.W. Milnor, Link groups, Annals of Math. 59 (1954), 177-195. MR 17:70e

[M57]
J.W. Milnor, Isotopy of links, in Algebraic Geometry and Topology (Fox, Spencer and Tucker, eds.), Princeton Univ. Press, 1957, 280-306. MR 19:1070c

[M87]
K. Murasugi, The Jones polynomial and classical conjectures in knot theory, Topology 26 (1987), 187-194. MR 88m:57010

[R32]
K. Reidemeister, Knotentheorie, Springer, Berlin, 1932.

[R93]
D. Roseman, Twisting and turning in four dimensions, video made at the Geometry Center, 1993.

[S66]
N.F. Smythe, Boundary links in Topology Seminar, Wisconsin 1965 (R.H. Bing, ed.), Annals of Math. Study 60, Princeton Univ. Press, Princeton, 1966, 69-72. MR 34:1974

[S77]
N. Stoltzfus, Unraveling the integral knot concordance group, Memoirs of the Amer. Math. Soc. 192, Amer. Math. Soc., Providence, RI, 1977. MR 57:7616

[T76]
P.G. Tait, Recent Advances in Physical Sciences, 2nd ed., Macmillan and Co., London, 1876, 294.

[T77]
P.G. Tait, On knots, Trans. of the RSE 28 (1877), 145-190; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. I, Cambridge Univ. Press, Cambridge, 1898, 273-317.

[T84]
P.G. Tait, On knots. Part II, Trans. RSE 32 (1884-1885), 327-339; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. II, Cambridge Univ. Press, Cambridge, 1898, 318-333.

[T84$'$]
P.G. Tait, On knots. Part III, Trans. RSE 32 (1884-1885), 493-506; reprinted in: P.G. Tait, Collected Scientific Papers, Vol. II, Cambridge Univ. Press, Cambridge, 1898, 335-347.

[T85]
M.B. Thistlethwaite, Knot tabulations and related results, in Aspects of Topology, LMS Lecture Series 93, Cambridge Univ. Press, Cambridge, 1985, 1-76. MR 86j:57004

[T87]
M.B. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987), 297-309. MR 88h:57007

[W68]
F. Waldhausen, On irreducible $3$-manifolds which are sufficiently large, Annals of Math. 87 (1968), 56-88. MR 36:7146

[W87]
W. Whitten, Knot complements and groups, Topology 26 (1987), 41-44. MR 88f:57014

[W89]
E. Witten, Some geometric applications of quantum field theory, I, A.M.P. Congress, Swansea, 1988 (I. Davies, B. Simon and A. Truman, eds.), Institute of Physics, College Park, MD, 1989.

[W89$'$]
E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 90h:57009

Additional Information:

Reviewer(s):
Daniel S. Silver
Affiliation: University of South Alabama
Email: silver@jaguar1.usouthal.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 41 (2004), 135-147.

MSC (2000): Primary 57M25, 57Q45
DOI: 10.1090/S0273-0979-03-01000-0
PII: S 0273-0979(03)01000-0
Posted: October 30, 2003
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google