Book Review
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Book Information:
Author:
D. McDuff and D. Salamon
Title:
Introduction to symplectic topology
Additional book information:
Oxford Science,
1995,
viii + 425 pp.,
ISBN 0-19-851177-9,
$82.00$
V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391
Michèle Audin, The topology of torus actions on symplectic manifolds, Progress in Mathematics, vol. 93, Birkhäuser Verlag, Basel, 1991. Translated from the French by the author. MR 1106194, DOI 10.1007/978-3-0348-7221-8
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
Nicole Berline, Ezra Getzler, and Michèle Vergne, Heat kernels and Dirac operators, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 298, Springer-Verlag, Berlin, 1992. MR 1215720, DOI 10.1007/978-3-642-58088-8
K. Fukaya, K. Ono, Arnold Conjecture and Gromov-Witten invariant, Warwick preprint 29/1996, June 1996.
V. Guillemin, E. Lerman, S. Sternberg, Symplectic fibrations and multiplicity diagrams, Cambridge University Press (1996).
Victor Guillemin and Shlomo Sternberg, Symplectic techniques in physics, Cambridge University Press, Cambridge, 1984. MR 770935
H. Hofer, D. Salamon, $J$-holomorphic curves, Floer homology, and the general Arnold conjecture, in preparation.
Helmut Hofer and Eduard Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 1994. MR 1306732, DOI 10.1007/978-3-0348-8540-9
F. Lalonde, Energy and capacities in symplectic topology, in Proceedings of the 1993 Georgia International Topology Conference (AMS/IP Studies in Advanced Mathematics 2) (1997) Part I, 328-374.
François Lalonde and Dusa McDuff, The geometry of symplectic energy, Ann. of Math. (2) 141 (1995), no. 2, 349–371. MR 1324138, DOI 10.2307/2118524
G. Liu, G. Tian, Floer Homology and Arnold Conjecture, MIT preprint, August 1996.
Dusa McDuff and Dietmar Salamon, $J$-holomorphic curves and quantum cohomology, University Lecture Series, vol. 6, American Mathematical Society, Providence, RI, 1994. MR 1286255, DOI 10.1090/ulect/006
Dusa McDuff, Elliptic methods in symplectic geometry, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 311–358. MR 1039425, DOI 10.1090/S0273-0979-1990-15928-2
Y. Ruan, Virtual neighbourhoods and monopole equations, preprint (1996).
Claude Viterbo, Capacités symplectiques et applications (d’après Ekeland-Hofer, Gromov), Astérisque 177-178 (1989), Exp. No. 714, 345–362 (French). Séminaire Bourbaki, Vol. 1988/89. MR 1040580
Claude Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), no. 4, 685–710. MR 1157321, DOI 10.1007/BF01444643
Alan Weinstein, Lectures on symplectic manifolds, Regional Conference Series in Mathematics, No. 29, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976. MR 0464312
Alan Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971), 329–346 (1971). MR 286137, DOI 10.1016/0001-8708(71)90020-X
- V. Arnol’d, Mathematical methods of classical mechanics, Springer-Verlag (1978).
- M. Audin, The topology of torus actions on symplectic manifolds, Birkhäuser (Progress in Mathematics 93) (1991).
- M. Audin, J. Lafontaine (eds), Holomorphic curves in symplectic geometry, Birkhäuser (Progress in Mathematics 117) (1994).
- N. Berline, E. Getzler, M. Vergne, Heat kernels and Dirac operators, Springer-Verlag (1992).
- K. Fukaya, K. Ono, Arnold Conjecture and Gromov-Witten invariant, Warwick preprint 29/1996, June 1996.
- V. Guillemin, E. Lerman, S. Sternberg, Symplectic fibrations and multiplicity diagrams, Cambridge University Press (1996).
- V. Guillemin, S. Sternberg, Symplectic techniques in physics, Cambridge University Press (1984).
- H. Hofer, D. Salamon, $J$-holomorphic curves, Floer homology, and the general Arnold conjecture, in preparation.
- H. Hofer, E. Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser (Birkhäuser Advanced Texts: Basel Textbooks) (1994).
- F. Lalonde, Energy and capacities in symplectic topology, in Proceedings of the 1993 Georgia International Topology Conference (AMS/IP Studies in Advanced Mathematics 2) (1997) Part I, 328-374.
- F. Lalonde, D. McDuff, The geometry of symplectic energy, Ann. of Math. 141 (1995) 349-371.
- G. Liu, G. Tian, Floer Homology and Arnold Conjecture, MIT preprint, August 1996.
- D. McDuff, D. Salamon, J-holomorphic curves and quantum cohomology, American Math. Society (University Lecture Series 6) (1994).
- D. McDuff, Elliptic methods in symplectic geometry, Bulletin of the American Math. Society (N.S.) 23 (1990) 311-58.
- Y. Ruan, Virtual neighbourhoods and monopole equations, preprint (1996).
- C. Viterbo, Capacités symplectiques et applications, Séminaire Bourbaki 1988-89, exposé no. 714. Astérisque 177-8 (1989) 345-62.
- C. Viterbo, Symplectic topology as the geometry of generating functions, Math. Annalen 292 (1992), 685-710.
- A. Weinstein, Lectures on symplectic manifolds, American Mathematical Society (CBMS Conference Series 29) (1977).
- A. Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971) 329-46.
Review Information:
Reviewer:
Lisa Jeffrey
Affiliation:
McGill University
Email:
jeffrey@math.mcgill.ca
Journal:
Bull. Amer. Math. Soc.
34 (1997), 441-445
DOI:
https://doi.org/10.1090/S0273-0979-97-00726-X
Keywords:
Symplectic forms,
symplectic geometry,
symplectic topology
Review copyright:
© Copyright 1997
American Mathematical Society
