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Book Review

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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. 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 89m:57034
  • 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 95i:58005
  • 4. L. Baulieu and I. M. Singer, The topological sigma model, Commun. Math. Phys. 125 (1989), 227--237. MR 91b:81153
  • 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 90e:58047
  • 7. M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307--347. MR 87j:53053
  • 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. E. Witten, Topological sigma models, Commun. Math. Phys. 118 (1988), 411--449. MR 90b:81080
  • 15. ------, Two-dimensional gravity and intersection theory on moduli space, Surveys Differential Geom. 1 (1991), 243--310. MR 93e:32028
  • 16. S. T. Yau (ed.), Mathematical aspects of string theory, Adv. Ser. Math. Phys., vol. 1, World Scientific, Singapore, 1986. MR 89m:81001

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
MSC (1991): Primary 53C15; Secondary 81T20
DOI: https://doi.org/10.1090/S0273-0979-96-00668-4
Review copyright: © Copyright 1996 American Mathematical Society
American Mathematical Society