Book Review
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MathSciNet review:
1567959
Full text of review:
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This review is available free of charge.
Book Information:
Author:
Michael Atiyah
Title:
The geometry and physics of knots
Additional book information:
Cambridge Univ. Press, 1990, 75 pp., US$39.50. ISBN 0-521-39521-6.
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
Raoul Bott, Two new combinatorial invariants for polyhedra, Portugal. Math. 11 (1952), 35–40. MR 48820
S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), no. 2, 279–315. MR 710056
Robert MacPherson, The combinatorial formula of Gabrielov, Gel′fand and Losik for the first Pontrjagin class, Séminaire Bourbaki, 29e année (1976/77), Lecture Notes in Math., vol. 677, Springer, Berlin, 1978, pp. Exp. No. 497, pp. 105–124. MR 521763
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
Imre Lakatos, Proofs and refutations, Cambridge University Press, Cambridge-New York-Melbourne, 1976. The logic of mathematical discovery; Edited by John Worrall and Elie Zahar. MR 0479916
Vaughan F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 103–111. MR 766964, DOI 10.1090/S0273-0979-1985-15304-2
Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. MR 990772
- [1]
- J. W. Alexander, Topoligical invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928), 275. MR 1501429
- [2]
- R. Bott, Two new combinatorial invariants for polyhedra, Portugal. Math. 2 (1952), pp. 35-40. MR 0048820 (14:74d)
- [3]
- S. Donaldson, An application of gauge theory to the topology of four manifolds, J. Differential Geom. 18 (1983), 269; Polynomial invariants for smooth four-manifolds, Oxford preprint. MR 710056 (85c:57015)
- [4]
- R. MacPherson, The combinatorial formula of Gabrielov, Gelfand, and Losik for the first Pontrjagin class, Séminaire Bourbaki No. 497, Lecture Notes in Math., vol. 667, Berlin and New York, 1977. MR 521763 (81a:57022)
- [5]
- L. Kaufman, State models and the Jones polynomial, Topology, 26 (1987), 395-407. MR 899057 (88f:57006)
- [6]
- I. Lakatos, Proofs and refutations, Cambridge Univ. Press, London and New York, 1976. MR 0479916 (58:122)
- [7]
- V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 103-111. MR 766964 (86e:57006)
- [8]
- E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 990772 (90h:57009)
Review Information:
Reviewer:
Raoul Bott
Journal:
Bull. Amer. Math. Soc.
26 (1992), 182-188
DOI:
https://doi.org/10.1090/S0273-0979-1992-00251-3
