Bulletin of the American Mathematical Society

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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.

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

[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