Skip to main content
Log in

Examples of symplectic structures

  • Published:
Inventiones mathematicae Aims and scope

Summary

In this paper we construct symplectic forms\(\tilde \omega _k , k \geqq 0\), on a compact manifold\({\tilde Y}\) which have the same homotopy theoretic invariants, but which are not diffeomorphic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • [Ar] Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of the second order. J. Math. Pures Appl. (9),36, 235–249 (1957)

    Google Scholar 

  • [AS] Atiyah, M.F., Singer, I.M.: Index of elliptic operators III. Ann. Math.87, 546–604 (1968)

    Google Scholar 

  • [B] Banyaga, A.: Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique. Comment. Math. Helv.53, 174–227 (1978)

    Google Scholar 

  • [BJS] Bers, L., John, F., Schechter, M.: Partial differential equations. AMS Lectures in Appl. Math., vol. 3A, Am. Math. Soc., Providence, 1964

    Google Scholar 

  • [BKW] Boothby, W.M., Kobayashi, S., Wang, H.C.: A note on mappings and automorphisms of almost complex manifolds. Ann. Math.77, 329–334 (1963)

    Google Scholar 

  • [FU] Freed, M., Uhlenbeck, K.: Instantons and 4-manifolds, MSRI publications. Berlin-Heidelberg-New York: Springer, (1984)

    Google Scholar 

  • [G1] Gromov, M.: Pseudo-holomorphic curves on almost complex manifolds. Invent. math.82, 307–347 (1985)

    Google Scholar 

  • [G2] Gromov, M.: Partial differential relations. Ergebnisse der Math., 3. Folge, Band 9, Berlin-Heidelberg-New York: Springer, 1986

    Google Scholar 

  • [McD 1] McDuff, D.: Applications of convex integration to symplectic and contact geometry. Ann. Inst. Fourier (in press) (1986/7)

  • [McD 2] McDuff, D.: Examples of simply-connected symplectic non-Kählerian manifolds. J. Differ. Geom.20, 267–277 (1984)

    Google Scholar 

  • [Mo] Moser, J.: On the volume element on manifolds. Trans. Am. Math. Soc.120, 280–296 (1965)

    Google Scholar 

  • [MK] Morrow, J., Kodaira, K.: Complex manifolds. Holt, Rinehart, Winston, New York 1971

    Google Scholar 

  • [NW] Nijenhuis, A., Woolf, W.: Some integration problems in almost-complex and complex manifolds. Ann. Math.77, 424–489 (1963)

    Google Scholar 

  • [P] Pansu, P.: Pseudoholomorphic curves in symplectic manifolds. Preprint, Ecole Polytechnique at Palaiseau, 1986

  • [Sm] Smale, S.: An infinite dimensional version of Sard's theorem. Am. J. Math.87, 861–866 (1965)

    Google Scholar 

  • [W] Weinstein, A.: Symplectic manifolds and their Lagrangian submanifolds. Adv. Math.6, 329–346 (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by NSF grant no. DMS 8504355

Rights and permissions

Reprints and permissions

About this article

Cite this article

McDuff, D. Examples of symplectic structures. Invent Math 89, 13–36 (1987). https://doi.org/10.1007/BF01404672

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01404672

Keywords

Navigation