Skip to Main Content

Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

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


MathSciNet review: 1567720
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Gerhard Burde and Heiner Zieschang
Title: Knots
Additional book information: DeGruyter Studies in Mathematics, vol. 5, Walter DeGruyter, Berlin, New York, 1985, x+399 pp., $49.95. ISBN 0-89925-014-9.

Author: Louis H. Kauffman
Title: On knots
Additional book information: Annals of Mathematics Studies, vol. 115, Princeton University Press, Princeton, N.J., 1987, xv+480 pp., $50.00 ($18.95 paperback). ISBN 0-691-08434-3.

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

  • 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
  • [A2] J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. U. S. A. 10 (1923), 93-95.

  • Daniel Bennequin, Entrelacements et équations de Pfaff, Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982) Astérisque, vol. 107, Soc. Math. France, Paris, 1983, pp. 87–161 (French). MR 753131
  • Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
  • [B] W. Burau, Über Zopfgruppen und gleichsinnig verdrillte Verkettunger, Abh. Math. Sem. Hanischen Univ. 11 (1936), 179-186.

  • Joan S. Birman and Hans Wenzl, Braids, link polynomials and a new algebra, Trans. Amer. Math. Soc. 313 (1989), no. 1, 249–273. MR 992598, DOI 10.1090/S0002-9947-1989-0992598-X
  • [C] J. Conway, An enumeration of knots and links and some of their related properties, Computational Problems in Abstract Algebra, (Leech, ed. ), Pergamon Press, 1967.

  • P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 239–246. MR 776477, DOI 10.1090/S0273-0979-1985-15361-3
  • Jürg Fröhlich, Statistics of fields, the Yang-Baxter equation, and the theory of knots and links, Nonperturbative quantum field theory (Cargèse, 1987) NATO Adv. Sci. Inst. Ser. B: Phys., vol. 185, Plenum, New York, 1988, pp. 71–100. MR 1008276
  • [H] Mary Haseman, On knots, with a census of the amphicheirals with twelve crossings, Trans. Royal Soc. Edinburgh 52 (1918), 235-255.

  • V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335–388. MR 908150, DOI 10.2307/1971403
  • Louis H. Kauffman, Statistical mechanics and the Jones polynomial, Braids (Santa Cruz, CA, 1986) Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 263–297. MR 975085, DOI 10.1090/conm/078/975085
  • Louis H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), no. 3, 395–407. MR 899057, DOI 10.1016/0040-9383(87)90009-7
  • [Ki] T. Kirkman, The enumeration, description and construction of knots with fewer than 10 crossings, Trans. Roy. Soc. Edin. 32 (1885), 281-309.

    [L] C. N. Little, On knots, with a census for order 10, Trans. Conn. Acad. Sci. 18 (1885), 374-378.

    [Lo] D. D. Long, On the linear representations of braid groups, preprint 1987.

    [Ma] A. A. Markov, Über die freie Aquivalenz der gescholossenen Zopfe, Recueil Math. Moskau 1 (1936), 73-78.

  • H. R. Morton, Threading knot diagrams, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 2, 247–260. MR 817666, DOI 10.1017/S0305004100064161
  • [P] K. Perko, On 10 crossing knots, unpublished.

    [R] K. Reidemeister, Knotentheorie, Ergeb. Math. Grenzgeb., Springer-Verlag, 1932; English Translation by L. Boron, C. Christenson and B. Smith, 1983, University of Idaho, Moscow, Idaho.

    [Ta] P. G. Tait, On knots. I, II, and III, Scientific Papers, vol. 1, Cambridge Univ. Press, London, 1898, pp. 273-347.

  • W. Thurston, Hyperbolic geometry and $3$-manifolds, Low-dimensional topology (Bangor, 1979) London Math. Soc. Lecture Note Ser., vol. 48, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 9–25. MR 662424
  • William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524, DOI 10.1090/S0273-0979-1982-15003-0
  • [Th3] W. Thurston, Finite state algorithms for the braid groups, preprint 1987.

  • Shuji Yamada, The minimal number of Seifert circles equals the braid index of a link, Invent. Math. 89 (1987), no. 2, 347–356. MR 894383, DOI 10.1007/BF01389082

  • Review Information:

    Reviewer: Joan S. Birman
    Journal: Bull. Amer. Math. Soc. 19 (1988), 550-558
    DOI: https://doi.org/10.1090/S0273-0979-1988-15740-0