Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Dusa McDuff and Dietmar Salamon
Title: $J$-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

References [Enhancements On Off] (What's this?)

  • 1. 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,
  • 2. M. Audin, Cohomologie quantique, Séminaire Bourbaki, no. 806, 1995--96.
  • 3. Michèle Audin and Jacques Lafontaine (eds.), Holomorphic curves in symplectic geometry, Progress in Mathematics, vol. 117, Birkhäuser Verlag, Basel, 1994. MR 1274923
  • 4. 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.
  • 6. Andreas Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), no. 4, 575–611. MR 987770
  • 7. M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718,
  • 8. H. Hofer and D. Salamon, Floer homology and Novikov rings, preprint 1993.
  • 9. F. Lalonde and D. McDuff, $J$-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. Edward Witten, Topological sigma models, Comm. Math. Phys. 118 (1988), no. 3, 411–449. MR 958805
  • 15. 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
  • 16. S.-T. Yau (ed.), Mathematical aspects of string theory, Advanced Series in Mathematical Physics, vol. 1, World Scientific Publishing Co., Singapore, 1987. MR 915812

Review Information:

Reviewer: François Lalonde
Affiliation: Université du Québec à Montréal; Centre de Recherches Mathématiques (Université de Montréal)
Journal: Bull. Amer. Math. Soc. 33 (1996), 385-394
Review copyright: © Copyright 1996 American Mathematical Society