Book Review
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MathSciNet review:
1568003
Full text of review:
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Book Information:
Author:
Charles Nash
Title:
Differential topology and quantum field theory
Additional book information:
Academic Press, New York, 1991, 386 pp., US$59.95. ISBN 0-12-514075-4.
Selman Akbulut and John D. McCarthy, Casson’s invariant for oriented homology $3$-spheres, Mathematical Notes, vol. 36, Princeton University Press, Princeton, NJ, 1990. An exposition. MR 1030042, DOI 10.1515/9781400860623
M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523–615. MR 702806, DOI 10.1098/rsta.1983.0017
M. F. Atiyah, N. J. Hitchin, V. G. Drinfel′d, and Yu. I. Manin, Construction of instantons, Phys. Lett. A 65 (1978), no. 3, 185–187. MR 598562, DOI 10.1016/0375-9601(78)90141-X
M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), no. 1711, 425–461. MR 506229, DOI 10.1098/rspa.1978.0143
M. F. Atiyah and I. M. Singer, Dirac operators coupled to vector potentials, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), no. 8, , Phys. Sci., 2597–2600. MR 742394, DOI 10.1073/pnas.81.8.2597
S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), no. 2, 279–315. MR 710056
S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), no. 3, 257–315. MR 1066174, DOI 10.1016/0040-9383(90)90001-Z
S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR 1079726
Andreas Floer, An instanton-invariant for $3$-manifolds, Comm. Math. Phys. 118 (1988), no. 2, 215–240. MR 956166
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, Global gravitational anomalies, Comm. Math. Phys. 100 (1985), no. 2, 197–229. MR 804460
Edward Witten, Topological quantum field theory, Comm. Math. Phys. 117 (1988), no. 3, 353–386. MR 953828
Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. MR 990772
Edward Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys in differential geometry (Cambridge, MA, 1990) Lehigh Univ., Bethlehem, PA, 1991, pp. 243–310. MR 1144529
- [AM]
- S. Akbulut and J. McCarthy, Casson's invariant for oriented homology 3-spheres--an exposition, Math. Notes, vol. 36, Princeton Univ. Press, Princeton, NJ, 1990. MR 1030042 (90k:57017)
- [AB]
- M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser A 308 (1982), 523-615. MR 702806 (85k:14006)
- [ADHM]
- M. F. Atiyah, V. Drinfeld, N. J. Hitchin, and Yu. I. Manin, Construction of instantons, Phys. Lett. A 65 (1978), 185-187. MR 598562 (82g:81049)
- [AHS]
- M. F. Atiyah, N. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), 425-461. MR 506229 (80d:53023)
- [AS]
- M. F. Atiyah and I. M. Singer, Diracs operators coupled to vector potentials, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 2597-2600. MR 742394 (86g:58127)
- [D1]
- S. K. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geom. 18 (1983), 279-315. MR 710056 (85c:57015)
- [D2]
- -, Polynomial invariants for smooth 4-manifolds, Topology 29 (1990), 257-315. MR 1066174 (92a:57035)
- [DK]
- S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Univ. Press, 1990. MR 1079726 (92a:57036)
- [F]
- A. Floer, An instanton invariant for 3-manifolds, Comm. Math. Phys. 118 (1989), 215-240. MR 956166 (89k:57028)
- [J]
- V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985), 103-111. MR 766964 (86e:57006)
- [W1]
- E. Witten, Global gravitational anomalies, Comm. Math. Phys. 100 (1985), 197-229. MR 804460 (87k:58282)
- [W2]
- -, Topological quantum field theory, Comm. Math. Phys. 117 (1988), 353-386. MR 953828 (89m:57037)
- [W3]
- -, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-400. MR 990772 (90h:57009)
- [W4]
- -, Two-dimensional gravity and intersection theory on moduli space, Surveys in Differential Geom. (supplement to J. Differential Geom.) (1991), 243-310. MR 1144529 (93e:32028)
Review Information:
Reviewer:
Daniel S. Freed
Journal:
Bull. Amer. Math. Soc.
28 (1993), 153-157
DOI:
https://doi.org/10.1090/S0273-0979-1993-00340-9