Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Akio Kawauchi
Title: A survey of knot theory
Additional book information: Birkhäuser-Verlag, Basel, Boston, and Berlin, 1996, xxi+420 pp., ISBN 3-7643-5124-1, $89.50

References [Enhancements On Off] (What's this?)

  • 1. J. W. Alexander, Note on Riemann spaces. Bull. Amer. Math. Soc., Vol. 26 (1920), pp. 370-372.
  • 2. J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. USA, Vol. 9 (1923), pp. 539-549.
  • 3. J.W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc., Vol. 30 (1928), pp. 275-306.
  • 4. E. Artin, Theorie der zopfe, Hamburg Abh., Vol. 4 (1926), pp. 539-549.
  • 5. C. W. Ashley, The Ashley Book of Knots, Doubleday and Co. (1944).
  • 6. M. Ascher and R. Ascher, Code of the Quipu, University of Michigan Press, Ann Arbor (1981). MR 83h:01007
  • 7. M.F. Atiyah, The Geometry and Physics of Knots, (1990), Cambridge University Press. MR 92b:57008
  • 8. J. Birman, Braids, Links and Mapping Class Groups, Annals of Math. Studies, Vol. 82 (1974). MR 51:11477
  • 9. A. J. Casson and C. McA. Gordon, On slice knots in dimension three, In: Algebraic and Geometric Topology (Stanford 1976), pp. 39-53, Proc. Sympos. Pure Math., 32-II, (edited by J. Milgram), Amer. Math. Soc. (1983). MR 81g:57003
  • 10. J. H. Conway, An enumeration of knots and links and some of their algebraic properties, In: Computational Problems in Abstract Algebra, Proc. Conf. Oxford (1967) (edited by J. Leech), pp. 329-358; New York: Pergamon Press. MR 41:2661
  • 11. J. H. Conway and C. McA Gordon, Knots and links in spatial graphs, J. Graph Theory, Vol. 7 (1983), No. 4, pp. 445-453. MR 85d:57002
  • 12. R. H. Crowell and R. H. Fox, Introduction to Knot Theory, New York: Ginn and Co. (1963), or: Grad. Texts Math. 57, Berlin-Heidelberg-New York: Springer Verlag (1977). MR 26:4348; MR 56:3829
  • 13. J. Elffers and M. Schuyt, Cat's Cradle and Other String Figures, Penguin Books (1978).
  • 14. L. Euler, The Seven Bridges of Konigsburg, Presentation to the Russian Academy at St. Petersburg (1735).
  • 15. R. Fenn and C. Rourke, On Kirby's calculus of links, Topology, Vol. 18 (1979), pp. 539-549. MR 80c:57005
  • 16. R. H. Fox., A quick trip through knot theory, In Topology of Three Manifolds - Proceedings of 1961 Topology Institute at Univ. of Georgia, edited by M. K. Fort, pp. 120-167. Englewood Cliffs, N. J. : Prentice-Hall. MR 25:3522
  • 17. R. H. Fox and J. Milnor, Singularities of 2- spheres in 4 - space and cobordism of knots. Osaka J. Math., Vol. 3 (1966), pp. 539-549. MR 35:2273
  • 18. K. Fulves, Self-Working Rope Magic, Dover Pub. (1990).
  • 19. K. F. Gauss, Gauss Werke - 1833, K$\ddot{o}$niglichen Gesellschaft der Wissenshaften zu G$\ddot{o}$ttingen (1877). p. 605.
  • 20. C. A. Giller, A family of links and the Conway calculus, Trans. Amer. Math. Soc., Vol. 270, (1982), pp. 539-549. MR 83j:57001
  • 21. R. Hartley, The Conway potential function for links, Comment. Math. Helv., Vol. 58, (1983), pp. 539-549. MR 85h:57006
  • 22. V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc., Vol. 12 (1985), pp. 539-549. MR 86e:57006
  • 23. L. H. Kauffman, Branched coverings, open books and knot periodicity, Topology, Vol. 13 (1974), pp. 539-549. MR 51:11532
  • 24. L. H. Kauffman and W. D. Neumann, Products of knots, branched fibrations and sums of singularities. Topology, Vol. 16 (1977), pp. 539-549. MR 58:7644
  • 25. L. H. Kauffman, The Conway Polynomial, Topology, Vol. 20 (1981), pp. 539-549. MR 81m:57004
  • 26. L. H. Kauffman, Formal Knot Theory, Mathematical Notes No. 30 (1983), Princeton University Press. MR 85b:57006
  • 27. L. H. Kauffman, State models and the Jones polynomial, Topology, Vol. 26 (1987), pp. 539-549. MR 88f:57006
  • 28. L. H. Kauffman On Knots, Ann. of Math. Studies, Vol. 115, Princeton University Press (1987). MR 89c:57005
  • 29. L. H. Kauffman (editor), Knots and Applications, Vol. 6 in Series on K&E, World Scientific Pub. Co. (1995). MR 96g:57001
  • 30. R. Kirby, A calculus for framed links in $S^{3}$, Invent. Math., Vol. 45 (1978), pp. 539-549. MR 57:7605
  • 31. J. Levine, Knot cobordism groups in codimension two, Comment. Math. Helv., Vol. 44 (1969), pp. 539-549. MR 39:7618
  • 32. A. A. Markov, $\ddot{\textup{U}}$ber die freie aquivalenz geschlossener zopfe, Recueil Mathematique Moscou, Vol. 1, pp. 73-78.
  • 33. W. Menasco and M. Thistlethwaite, The classification of alternating links, Ann. of Math., Vol. 138, (1993), pp. 539-549. MR 95g:57015
  • 34. J. Milnor, On manifolds homeomorphic to the 7-sphere, Annals of Math., Vol. 64, No. 2, Sept. 1956, pp. 399-405. MR 18:498d
  • 35. J. Milnor, Singular Points of Complex Hypersurfaces, Ann. of Math. Studies Vol. 61 (1968), Princeton University Press, Princeton, New Jersey. MR 39:969
  • 36. K. Reidemeister, Knotentheorie, (1932) Ergeben. Math. Grenzgeb., Bd. 1; Berlin: Springer Verlag.
  • 37. N. Y. Reshetikhin and V. Turaev, Invariants of three manifolds via link polynomials and quantum groups, Invent. Math., Vol. 103 (1991), pp. 539-549. MR 92b:57024
  • 38. A. Stasiak, V. Katritch and L. H. Kauffman, Ideal Knots, (1998), Vol. 19 in Series on K&E, World Sci. Pub.
  • 39. H. Seifert, Über das geschlecht von knoten, Math. Ann., Vol. 110, (1934), pp. 539-549.
  • 40. E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys., Vol. 121 (1989), pp. 539-549. MR 90h:57009

Review Information:

Reviewer: Louis H. Kauffman
Affiliation: University of Illinois at Chicago
Email: kauffman@uic.edu
Journal: Bull. Amer. Math. Soc. 36 (1999), 539-549
MSC (1991): Primary 57M25
DOI: https://doi.org/10.1090/S0273-0979-99-00797-1
Published electronically: July 29, 1999
Review copyright: © Copyright 1999 American Mathematical Society
American Mathematical Society