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Book Review
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Book Information
Author(s):
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(s):
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:
- [A1] J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928), 275-306. MR 1501429
- [A2] J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. U. S. A. 10 (1923), 93-95.
- [Be] D. Bennequin, Entrelacements et equations de Pfaff, Astérisque 107-108 (1983), 87-161. MR 753131
- [Bi] J. S. Birman, Braid, links and mapping class groups, Ann. of Math. Studies no. 82, Princeton Univ. Press, Princeton, N. J., 1974. MR 375281
- [B] W. Burau, Über Zopfgruppen und gleichsinnig verdrillte Verkettunger, Abh. Math. Sem. Hanischen Univ. 11 (1936), 179-186.
- [B-W] J. S. Birman and H. Wenzl, Braids, link polynomials and a new algebra, preprint, 1987. MR 992598
- [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.
- [FYHLMO] P. Freyd and D. Yetter; J. Hoste; W. B. R. Lickorish, K. Millet; and A. Ocneaunu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N. S. ) 12 (1985), 239-246. MR 776477
- [F] J. Frohlich, Statistics of fields, the Yang-Baxter equation, and the theory of knots and links, preprint, ETH, Zurich. MR 1008276
- [H] Mary Haseman, On knots, with a census of the amphicheirals with twelve crossings, Trans. Royal Soc. Edinburgh 52 (1918), 235-255.
- [J] V. F. R. Jones, Hecke algebra representations of link polynomials and braid groups, Ann. of Math. (2) 126 (1987), 335-388. MR 908150
- [Ka1] L. Kauffman, Statistical mechanics and the Jones polynomial, Braids, Contemp. Math. (to appear). MR 975085
- [Ka2] L. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407. MR 899057
- [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.
- [Mo] H. Morton, Threading knot diagrams, Math. Proc. Cambridge Philos. Soc. 99 (1986), 247-260. MR 817666
- [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.
- [Th1] W. Thurston, The geometry and topology of three manifolds, preprint 1982. MR 662424
- [Th2] W. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N. S. ) 6 (1982), 357-381. MR 648524
- [Th3] W. Thurston, Finite state algorithms for the braid groups, preprint 1987.
- [Y] S. Yamada, The minimal number of Seifert circles equals the braid index of a link, Invent. Math. 89 (1987), 347-356. MR 894383
Additional Information:
Reviewer(s):
Joan S.
Birman
Review Information:
Journal:
Bull. Amer. Math. Soc.
19
(1988),
550-558.
DOI:
10.1090/S0273-0979-1988-15740-0
PII:
S 0273-0979(1988)15740-0
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