Book Review
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Book Information:
Authors:
Dusa McDuff and
Dietmar Salamon
Title:
-holomorphic curves and quantum cohomology
Additional book information:
University Lecture Series, vol. 6, Amer. Math. Soc.,
Providence, RI,
1994,
vii+207 pp.,
ISBN 0-8218-0332-8
Michael Atiyah, New invariants of $3$- and $4$-dimensional manifolds, The mathematical heritage of Hermann Weyl (Durham, NC, 1987) Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, RI, 1988, pp. 285–299. MR 974342, DOI 10.1090/pspum/048/974342
2. M. Audin, Cohomologie quantique, Séminaire Bourbaki, no. 806, 1995--96.
Michèle Audin and Jacques Lafontaine (eds.), Holomorphic curves in symplectic geometry, Progress in Mathematics, vol. 117, Birkhäuser Verlag, Basel, 1994. MR 1274923, DOI 10.1007/978-3-0348-8508-9
L. Baulieu and I. M. Singer, The topological sigma model, Comm. Math. Phys. 125 (1989), no. 2, 227–237. MR 1016870
5. R. P. Feynman and A. R. Hibbs, Quantum mechanics and paths integrals, McGraw-Hill, New York, 1965.
Andreas Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), no. 4, 575–611. MR 987770
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718, DOI 10.1007/BF01388806
8. H. Hofer and D. Salamon, Floer homology and Novikov rings, preprint 1993.
9. F. Lalonde and D. McDuff, 
-curves and the classification of rational and ruled symplectic 4-manifolds (Proc. Symplectic Topology Program, Newton Institute), Cambridge Univ. Press, to appear.
10. S. Piunikhin, D. Salamon, and M. Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, preprint 1995.
11. Y. Ruan, Topological sigma model and Donaldson type invariants in Gromov theory, preprint 1993.
12.Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, J. Differential Geom., to appear.
13. C. Taubes, The Seiberg-Witten and the Gromov invariants, preprint 1995.
Edward Witten, Topological sigma models, Comm. Math. Phys. 118 (1988), no. 3, 411–449. MR 958805
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
S.-T. Yau (ed.), Mathematical aspects of string theory, Advanced Series in Mathematical Physics, vol. 1, World Scientific Publishing Co., Singapore, 1987. MR 915812, DOI 10.1142/0383
- 1.
- M. Atiyah, New invariants of three and four-dimensional manifolds, The Mathematical Heritage of H. Weyl (R. Wells, ed.), Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, RI, 1988. MR 0974342
- 2.
- M. Audin, Cohomologie quantique, Séminaire Bourbaki, no. 806, 1995--96.
- 3.
- M. Audin and J. Lafontaine (eds.), Holomorphic curves in symplectic geometry, Progress in Math., vol. 117, Birkhäuser, Basel and Boston, MA, 1994. MR 1274923
- 4.
- L. Baulieu and I. M. Singer, The topological sigma model, Commun. Math. Phys. 125 (1989), 227--237. MR 1016870
- 5.
- R. P. Feynman and A. R. Hibbs, Quantum mechanics and paths integrals, McGraw-Hill, New York, 1965.
- 6.
- A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575--611. MR 0987770
- 7.
- M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307--347. MR 0809718
- 8.
- H. Hofer and D. Salamon, Floer homology and Novikov rings, preprint 1993.
- 9.
- F. Lalonde and D. McDuff, -curves and the classification of rational and ruled symplectic 4-manifolds (Proc. Symplectic Topology Program, Newton Institute), Cambridge Univ. Press, to appear.
- 10.
- S. Piunikhin, D. Salamon, and M. Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, preprint 1995.
- 11.
- Y. Ruan, Topological sigma model and Donaldson type invariants in Gromov theory, preprint 1993.
- 12.
- Y. Ruan and G. Tian, A mathematical theory of quantum cohomology, J. Differential Geom., to appear.
- 13.
- C. Taubes, The Seiberg-Witten and the Gromov invariants, preprint 1995.
- 14.
- E. Witten, Topological sigma models, Commun. Math. Phys. 118 (1988), 411--449. MR 0958805
- 15.
- ------, Two-dimensional gravity and intersection theory on moduli space, Surveys Differential Geom. 1 (1991), 243--310. MR 1144529
- 16.
- S. T. Yau (ed.), Mathematical aspects of string theory, Adv. Ser. Math. Phys., vol. 1, World Scientific, Singapore, 1986. MR 0915812
Review Information:
Reviewer:
François Lalonde
Affiliation:
Université du Québec à Montréal;
Centre de Recherches Mathématiques (Université de Montréal)
Email:
flalonde@math.uqam.ca, lalonde@crm.umontreal.ca
Journal:
Bull. Amer. Math. Soc.
33 (1996), 385-394
DOI:
https://doi.org/10.1090/S0273-0979-96-00668-4
Review copyright:
© Copyright 1996
American Mathematical Society
