Book Review
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MathSciNet review:
1568116
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Book Information:
Author:
V. F. R. Jones
Title:
Subfactors and knots
Additional book information:
CBMS Regional Conference Series in Mathematics, vol. 80, American Mathematical Society, Providence, RI, ix\,+\,113 pp., US$43{.}00. ISBN 0-8218-0729-3.
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
M. F. Atiyah, The geometry and physics of knots, Miniconference on Geometry and Physics (Canberra, 1989) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 22, Austral. Nat. Univ., Canberra, 1989, pp. 1–17. MR 1027859
Rodney J. Baxter, Exactly solved models in statistical mechanics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1982. MR 690578
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
J. H. Conway, An enumeration of knots and links, and some of their algebraic properties, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 329–358. MR 0258014
R. H. Fox, A quick trip through knot theory, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 120–167. MR 0140099
Ralph H. Fox and John W. Milnor, Singularities of $2$-spheres in $4$-space and cobordism of knots, Osaka Math. J. 3 (1966), 257–267. MR 211392
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
V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127
[10] -, A polynomial invariant for links via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 129 (1987), 103-112.
V. F. R. Jones, A new knot polynomial and von Neumann algebras, Notices Amer. Math. Soc. 33 (1986), no. 2, 219–225. MR 830613
V. F. R. Jones, On knot invariants related to some statistical mechanical models, Pacific J. Math. 137 (1989), no. 2, 311–334. MR 990215
Louis H. Kauffman, The Conway polynomial, Topology 20 (1981), no. 1, 101–108. MR 592573, DOI 10.1016/0040-9383(81)90017-3
[14] -, Formal knot theory, Math. Notes, vol 30, Princeton Univ. Press, Princeton, NJ, 1983.
[15] -, On knots, Ann. of Math. Stud., vol. 115, Princeton Univ. Press, Princeton, NJ, 1987.
Louis H. Kauffman, Knots and physics, 2nd ed., World Scientific Publishing Co., Inc., River Edge, NJ, 1993. MR 1306280
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
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, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990), no. 2, 417–471. MR 958895, DOI 10.1090/S0002-9947-1990-0958895-7
Louis H. Kauffman and Sóstenes L. Lins, Temperley-Lieb recoupling theory and invariants of $3$-manifolds, Annals of Mathematics Studies, vol. 134, Princeton University Press, Princeton, NJ, 1994. MR 1280463, DOI 10.1515/9781400882533
John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
John W. Milnor, Infinite cyclic coverings, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 115–133. MR 0242163
Józef H. Przytycki and PawełTraczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1988), no. 2, 115–139. MR 945888
[24] K. Reidemeister, Knotentheorie, Chelsea Publ. Co., New York, 1984; Julius Springer, Berlin, 1932.
N. Reshetikhin and V. G. Turaev, Invariants of $3$-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597. MR 1091619, DOI 10.1007/BF01239527
Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. MR 990772
- [1]
- J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 20 (1923), 275-306. MR 1501429
- [2]
- M. F. Atiyah, The geometry and physics of knots, Cambridge Univ. Press, London, 1990. MR 1027859 (91b:57003)
- [3]
- R. J. Baxter, Exactly solved models in statistical mechanics, Academic Press, New York, 1982. MR 690578 (86i:82002a)
- [4]
- J. S. Birman, Braids, links and mapping class groups, Ann. of Math. Stud., vol. 92, Princeton Univ. Press, Princeton, NJ, 1974. MR 0375281 (51:11477)
- [5]
- J. H. Conway, An enumeration of knots and links and some of their algebraic properties, Computational Problems in Abstract Algebra, Pergammon Press, New York, 1970, pp. 329-358. MR 0258014 (41:2661)
- [6]
- R. H. Fox, A quick trip through knot theory, Topology of Manifolds (M. K. Fort, ed.), Prentice-Hall, Englewood Cliffs, NJ, 1962, pp. 120-167. MR 0140099 (25:3522)
- [7]
- R. H. Fox and J. W. Milnor, Singularities of 2-spheres in 4-space and cobordism of knots, Osaka J. Math. 3 (1966), 257-267. MR 0211392 (35:2273)
- [8]
- P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, C. K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 239-246. MR 776477 (86e:57007)
- [9]
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), 1-25. MR 696688 (84d:46097)
- [10]
- -, A polynomial invariant for links via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 129 (1987), 103-112.
- [11]
- -, A new knot polynomial and von Neumann algebras, Notices of Amer. Math. Soc. 33 (1986), 219-225. MR 830613 (87d:57007)
- [12]
- -, On knots invariants related to some statistical mechanics models, Pacific J. Math. 137 (1989), 311-334. MR 990215 (89m:57005)
- [13]
- L. H. Kauffman, The Conway polynomial, Topology 20 (1980), 101-108. MR 592573 (81m:57004)
- [14]
- -, Formal knot theory, Math. Notes, vol 30, Princeton Univ. Press, Princeton, NJ, 1983.
- [15]
- -, On knots, Ann. of Math. Stud., vol. 115, Princeton Univ. Press, Princeton, NJ, 1987.
- [16]
- -, Knots and physics, World Scientific Press, Singapore, 1991, 1993. MR 1306280 (95i:57010)
- [17]
- -, State models and the Jones polynomial, Topology 26 (1987), 395-407. MR 899057 (88f:57006)
- [18]
- -, Statistical mechanics and the Jones polynomial, Proceedings of the 1986 Santa Cruz Conference of the Artin Braid Group, Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, pp. 263-297. MR 975085 (89j:57002)
- [19]
- -, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990), 417-471. MR 958895 (90g:57007)
- [20]
- L. H. Kauffman and S. Lins, Temperley Lieb recoupling theory and invariants of 3-manifolds, Ann. of Math. Stud., Princeton Univ. Press, Princeton, NJ, 1994 (to appear). MR 1280463 (95c:57027)
- [21]
- J. W. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., Princeton Univ. Press, Princeton, NJ, 1968. MR 0239612 (39:969)
- [22]
- -, Infinite cyclic coverings, Topology of Manifolds (Michigan State University 1967), Prindle, Weber, and Schmidt, Boston, 1968. MR 0242163 (39:3497)
- [23]
- Przytycki and Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1987), 115-139. MR 945888 (89h:57006)
- [24]
- K. Reidemeister, Knotentheorie, Chelsea Publ. Co., New York, 1984; Julius Springer, Berlin, 1932.
- [25]
- N. Y. Reshetikhin and V. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597. MR 1091619 (92b:57024)
- [26]
- D. Rolfson, Knots and links, Publish or Perish Press, Cambridge, MA, 1976. MR 0515288 (58:24236)
- [27]
- E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 990772 (90h:57009)
Review Information:
Reviewer:
Louis H. Kauffman
Journal:
Bull. Amer. Math. Soc.
31 (1994), 147-154
DOI:
https://doi.org/10.1090/S0273-0979-1994-00509-9