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Book Review
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Book Information
Author(s):
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
References:
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- J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. \textbf{20} (1923), 275--306.
- [2]
- M. F. Atiyah, The geometry and physics of knots, Cambridge Univ. Press, London, 1990.
- [3]
- R. J. Baxter, Exactly solved models in statistical mechanics, Academic Press, New York, 1982.
- [4]
- J. S. Birman, \emph{Braids, links and mapping class groups}, Princeton Univ. Press, Princeton, NJ, 1974.
- [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.
- [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.
- [7]
- R. H. Fox and J. W. Milnor, Singularities of \RM 2-spheres in \RM 4-space and cobordism of knots, Osaka J. Math. \textbf{3} (1966), 257--267.
- [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.) \textbf{12} (1985), 239--246.
- [9]
- V. F. R. Jones, Index for subfactors, Invent. Math. \textbf{72} (1983), 1--25.
- [10]
- V. F. R. Jones, A polynomial invariant for links via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) \textbf{129} (1987), 103--112.
- [11]
- V. F. R. Jones, A new knot polynomial and von Neumann algebras, Notices of Amer. Math. Soc. \textbf{33} (1986), 219--225.
- [12]
- V. F. R. Jones, On knots invariants related to some statistical mechanics models, Pacific J. Math. \textbf{137} (1989), 311--334.
- [13]
- L. H. Kauffman, The Conway polynomial, Topology \textbf{20} (1980), 101--108.
- [14]
- L. H. Kauffman, \emph{Formal knot theory}, Princeton Univ. Press, Princeton, NJ, 1983.
- [15]
- L. H. Kauffman, \emph{On knots}, Princeton Univ. Press, Princeton, NJ, 1987.
- [16]
- L. H. Kauffman, Knots and physics, World Scientific Press, Singapore, 1991, 1993.
- [17]
- L. H. Kauffman, State models and the Jones polynomial, Topology \textbf{26} (1987), 395--407.
- [18]
- L. H. Kauffman, \emph{Statistical mechanics and the Jones polynomial}, Proceedings of the 1986 Santa Cruz Conference of the Artin Braid Group, Amer. Math. Soc., Providence, RI pp.~263--297.
- [19]
- L. H. Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. \textbf{318} (1990), 417--471.
- [20]
- L. H. Kauffman and S. Lins, \emph{Temperley Lieb recoupling theory and invariants of \RM 3-manifolds}, Princeton Univ. Press, Princeton, NJ, 1994.
- [21]
- J. W. Milnor, \emph{Singular points of complex hypersurfaces}, Princeton Univ. Press, Princeton, NJ, 1968.
- [22]
- J. W. Milnor, Infinite cyclic coverings, Topology of Manifolds (Michigan State University 1967), Prindle, Weber, and Schmidt, Boston, 1968.
- [23]
- Przytycki and Traczyk, Invariants of links of Conway type, Kobe J. Math. \textbf{4} (1987), 115--139.
- [24]
- K. Reidemeister, Knotentheorie, Chelsea Publ. Co., New York, 1984.
- [25]
- N. Y. Reshetikhin and V. Turaev, Invariants of \RM 3-manifolds via link polynomials and quantum groups, Invent. Math. \textbf{103} (1991), 547--597.
- [26]
- D. Rolfson, Knots and links, Publish or Perish Press, Cambridge, MA, 1976.
- [27]
- E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. \textbf{121} (1989), 351--399.
Additional Information:
Reviewer(s):
Louis H.
Kauffman
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
147-154.
DOI:
10.1090/S0273-0979-1994-00509-9
PII:
S 0273-0979(1994)00509-9
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