Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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



Elliptic methods in symplectic geometry

Author: Dusa McDuff
Journal: Bull. Amer. Math. Soc. 23 (1990), 311-358
MSC (1985): Primary 53C15, 58E05, 58F05
MathSciNet review: 1039425
Full-text PDF

References | Similar Articles | Additional Information

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

  • [A1] V. I. Arnold, Mathematical methods of classical mechanics, Springer-Verlag, Berlin, Heidelberg, New York, 1978. MR 690288
  • [A2] V. I. Arnold, First steps in symplectic topology, Russian Math. Surveys 41 (6), (1986), 1-21. MR 890489
  • [At] M. Atiyah, New invariants of 3 and 4 dimensional manifolds, Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, R.I., 1988, 285-299. MR 974342
  • [AB] M. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Proc. Roy. Soc. London Ser. A 308 (1982), 523-615. MR 702806
  • [BP] L. Bates and G. Peschke, A remarkable symplectic structure, preprint, Calgary, 1989. MR 1072917
  • [Be] D. Bennequin, Problèmes elliptiques, surfaces de Riemann, et structures symplectiques, Sém. Bourbaki 1985-86 #657, Astérisque 145-146 (1987), 4, 111-136. MR 880029
  • [B] R. Bott, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (1982), 331-358. MR 663786
  • [CZ] C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math. 73 (1983), 33-49. MR 707347
  • [E1] Ya. Eliashberg, A theorem on the structure of wave fronts, Functional Anal. Appl. 21 (1987), 65-72. MR 911776
  • [E2] Ya. Eliashberg, Three lectures on symplectic topology, Conference at Cala Gonone, Italy, 1988.
  • [E3] Ya. Eliashberg, On symplectic manifolds which are bounded by standard contact spheres, J. Differential Geom. (to appear). MR 1085141
  • [EH] I. Ekeland and H. Hofer, Symplectic topology and Hamiltonian dynamics I, Math. Z. 200 (1989), 355-378; Part II: Math. Z. (to appear). MR 978597
  • [F1] A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. XLI (1988), 775-813. MR 948771
  • [F2] A. Floer, A relative Morse index for the symplectic action, Comm. Pure Appl. Math. XLI (1988), 393-407. MR 933228
  • [F3] A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), 513-547. MR 965228
  • [F4] A. Floer, An instanton invariant for 3-manifolds, Comm. Math. Phys. 118 (1988), 215-240. MR 956166
  • [F5] A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), 575-611. MR 987770
  • [F6] A. Floer, Witten's complex and infinite dimensional Morse theory, J. Differential Geom. 30 (1989), 207-221. MR 1001276
  • [F7] A. Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math. XLII (1989), 335-357. MR 990135
  • [FHV] A. Floer, H. Hofer and C. Viterbo, The Weinstein conjecture in Px C1, Math Zeitschrift 203 (1990), 469-482. MR 1038712
  • [FU] D. Freed and K. Uhlenbeck, Instantons and four-manifolds, Publ. MSRI, vol. 1, Springer-Verlag, New York, 1984. MR 757358
  • [Gi] A. Giventhal, Nonlinear Maslov index and Lagrangian intersections, preprint, 1990. MR 1171907
  • [GS] R. Greene and K. Shiohama, Diffeomorphisms and volume-preserving embeddings of non-compact manifolds, Trans. Amer. Math. Soc. 255 (1979), 403-414. MR 542888
  • [GH] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978. MR 507725
  • [G1] M. Gromov, Pseudo-holomorphic curves on almost complex manifolds, Invent. Math. 82 (1985), 307-347. MR 0809718
  • [G2] M. Gromov, Partial differential relations, Ergebnisse der Math, Springer-Verlag, Berlin, Heidelberg, New York, 1986. MR 864505
  • [G3] M. Gromov, Soft and hard symplectic geometry, Proceedings of the ICM at Berkeley, 1986, 1987, vol. 1, Amer. Math. Soc., Providence, R.I., pp. 81-98. MR 934217
  • [Gr] A. Grothendieck, Sur las classification des fibrés holomorphies sur la sphère de Riemann, Amer. J. Math. 76 (1957), 121-138. MR 87176
  • [H1] H. Hofer, On Ljusternik-Schnirelman theory for Lagrangian intersections, Ann. Inst. H. Poincaré Anal. NonLinèaire (1988). MR 970850
  • [H2] H. Hofer, Recent progress in symplectic geometry, Nonlinear functional analysis, edited by P. S. Milojevic, Marcel Dekker, New York (to appear). MR 1025808
  • [H3] H. Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh (special volume on the occasion of J. Hale's 60th birthday) (to appear). MR 1059642
  • [HV1] H. Hofer and C. Viterbo, The Weinstein conjecture for compact manifolds and related results, preprint, 1989.
  • [HV2] H. Hofer and C. Viterbo, The Weinstein conjecture for cotangent bundles and related results, Ann. Scuola Norm. Sup. Pisa Cl. Sci., vol. 15, 1988, 411-446. MR 1015801
  • [HZ] H. Hofer and E. Zehnder, A new capacity for symplectic manifolds (to appear in the Proceedings of the Conference on the occasion of J. Moser's 60th birthday). MR 1039354
  • [K] W. Klingenberg, Lectures on closed geodesics, Grundlehren Math. Wiss., vol. 230, Springer-Verlag, Berlin, Heidelberg, New York, 1978. MR 478069
  • [Ko] J. Kollar, The structure of algebraic threefolds, an introduction to Mori's program, Bull. Amer. Math. Soc. 17 (1987), 211-277. MR 903730
  • [Kr] A. Krygin, Continuation of diffeomorphisms preserving volume, Functional Anal. Appl. 5 (1971), 147-150. MR 368067
  • [L] H. B. Lawson, Minimal varieties in real and complex geometry, Sem. Math. Sup., vol. 57, Presses Univ. Montreal, Montreal, 1974. MR 474148
  • [MD1] D. McDuff, Symplectic diffeomorphisms and the flux homomorphism, Invent. Math. 77 (1984), 353-366. MR 752824
  • [MD2] D. McDuff, Examples of symplectic structures, Invent. Math. 89 (1987), 13-36. MR 892186
  • [MD3] D. McDuff, Rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc. (to appear). MR 1171905
  • [M] J. Moser, On the volume elements on manifolds, Trans. Amer. Math. Soc. 120 (1965), 280-296. MR 182927
  • [O1] Y.-G. Oh, Floer cohomology of symplectic Lagrangian submanifolds, preprint, (NYU) 1989.
  • [O2] Y.-G. Oh, Removal of boundary singularities of pseudo-holomorphic curves with Lagrangian boundary conditions, preprint NYU, 1990. MR 1135926
  • [P] P. Pansu, Pseudo-holomorphic curves in symplectic manifolds, preprint, École Polytechnique, Palaiseau, 1986.
  • [S] D. Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990), 113-140. MR 1045282
  • [SZ] D. Salamon and E. Zehnder, Floer homology, the Maslov index and periodic orbits of Hamiltonian equations, Analysis Et Cetera (P. H. Rabinowitz and E. Zender, eds.), Academic Press, 1990, 573-600. MR 1039363
  • [Sm] S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1973), 213-221. MR 185604
  • [T] C. Taubes, Moduli spaces and homotopy theory, Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, R.I., 1988, 301-315. MR 974343
  • [V1] C. Viterbo, Capacités symplectiques et applications, Sem. Bourb. #714, June 1989.
  • [V2] C. Viterbo, Recent progress in periodic orbits of autonomous Hamiltonian systems, Non-Linear Functional Analysis (P. S. Milojevic, Marcel Dekker, eds.) (to appear). MR 1025811
  • [Wn1] A. Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Adv. in Math. 6 (1971), 329-346. MR 286137
  • [Wn2] A. Weinstein, On extending the Conley-Zehnder fixed point theorem to other manifolds, Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, R.I., 1986, 451-454. MR 843640
  • [W1] E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), 661-692. MR 683171
  • [W2] E. Witten, Geometry and quantum field theory, Amer. Math. Soc. Lecture, summer meeting, 1988. MR 1184624
  • [Wo] J. G. Wolfson, Gromov's compactness of pseudo-holomorphic curves and symplectic geometry, J. Differential Geom. 28 (1988), 383-405. MR 965221

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 53C15, 58E05, 58F05

Retrieve articles in all journals with MSC (1985): 53C15, 58E05, 58F05

Additional Information


American Mathematical Society