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Book Review
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Book Information
Author(s):
Dusa McDuff and Dietmar Salamon
Title:
 -holomorphic curves and symplectic topology
Additional book information:
Colloquium Publications, vol. 52,
Amer. Math. Soc., Providence, RI,
2004,
xii+669,
US$99.00,
ISBN 0-8218-3485-1
References:
-
- 1.
- Arnold, V. I., Sur une proprieté topologique des applications globalement canonique de la mécanique classique, C.R. Acad. Sci. Paris 261 (1965), 3719-3722. MR 0193645 (33:1861)
- 2.
- Chekanov, Yu., Differential Algebra of Legendrian Links, Invent. Math. 150 (2002), 441-483. MR 1946550 (2003m:53153)
- 3.
- Conley, C. C., Zehnder, E., The Birkhoff-Lewis fixed-point theorem and a conjecture of V. I. Arnold, Invent. Math., 73 (1983), 3-49. MR 0707347 (85e:58044)
- 4.
- Dubrovin, B., Geometry of 2D topological field theories, Springer Lecture Notes in Math. 1620 (1996), 120-348. MR 1397274 (97d:58038)
- 5.
- Eliashberg, Y., Invariants in Contact Topology, Proc. ICM-98, Berlin, Doc. Math., 327-338. MR 1648083 (2000a:57068)
- 6.
- Eliashberg, Y., Givental, A., Hofer, H., Introduction to Symplectic Field Theory in Geom. Funct. Anal., Special volume, Part II (2000), 560-673. MR 1826267 (2002e:53136)
- 7.
- Floer, A., Morse theory for Lagrangian intersections, J. Diff. Geom., 28 (1988), 513-547. MR 0965228 (90f:58058)
- 8.
- Floer, A., The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math 41 (1988), 775-813. MR 0948771 (89g:58065)
- 9.
- Fukaya, K., Oh, Y-G., Ono, K., Ohta, H., Lagrangian intersection Floer theory - anomaly and obstruction, to be published in Int. Press.
- 10.
- Givental, A., The mirror formula for quintic threefolds, Amer. Math. Soc. Transl. Ser. 2, 196 (1999), 49-62. MR 1736213 (2000j:14083)
- 11.
- Givental, A., Semisimple Frobenius structures at higher genus, arXiv math. AG/0008067.
- 12.
- Gromov, M., Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 0809718 (87j:53053)
- 13.
- Hofer, H., On the topological properties of symplectic maps, Proc. Royal Soc. Edinburgh 115 (1990), 25-38. MR 1059642 (91h:58042)
- 14.
- Kontsevich, M., Enumeration of rational curves via torus action, in The moduli space of curves, Progress in Math. 129, Birkhäuser, 1995. MR 1363062 (97d:14077)
- 15.
- Lalonde, F., Sikorav, J.-C., Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents, Comm. Math. Helv. 66 (1991), 18-33. MR 1090163 (92f:58060)
- 16.
- McDuff, D., The structure of rational and ruled symplectic
 -manifolds, J. Amer. Math. Soc. 3 (1990), 679-712. MR 1049697 (91k:58042) - 17.
- McDuff, D., Salamon, D.,
 -holomorphic curves and quantum cohomology, Amer. Math. Soc. Univ. Lect. Ser. 6, 1994. MR 1286255 (95g:58026) - 18.
- Ozsváth, P., Szabó, Z., Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), 1027-1158. MR 2113019 (2006b:57016)
- 19.
- Polterovich, L., The Geometry of the Group of Symplectic Diffeomorphisms, Birkhäuser, 2001. MR 1826128 (2002g:53157)
- 20.
- Taubes, C. H., The Seiberg-Witten and Gromov invariants for symplectic
 -manifolds, First Internat. Press Lect. Ser. 2, International Press, Somerville, MA, 2000. MR 1798809 (2002j:53115) - 21.
- Weinstein, A., On the hypothesis of Rabinowitz' periodic orbit theorems, J. Diff. Eq. 33 (1979), 353-358. MR 0543704 (81a:58030b)
Additional Information:
Reviewer(s):
Yakov
Eliashberg
Affiliation:
Stanford University
Email:
eliash@math.stanford.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
44
(2007),
309-315.
MSC
(2000):
Primary 53D05, 53D45, 53D35, 57R17, 37J05, 32Q65;
Secondary 53D12, 53D40, 58J05, 14N35
PII:
S 0273-0979(06)01132-3
Posted:
December 1, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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