Siberian Mathematical Journal

, Volume 41, Issue 2, pp 204–217 | Cite as

On nonformal simply-connected symplectic manifolds

  • I. K. Babenko
  • I. A. Taîmanov


Minimal Model Symplectic Form Symplectic Manifold Symplectic Structure Triple Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gromov M. L., “A topological technique for the construction of solutions of differential equations and inequalities,” in: Actes Congrés Intern. Math. (Nice, 1970), Gauthier-Villars, Paris, 1971,2, pp. 221–225.Google Scholar
  2. 2.
    Tischler D., “Closed 2-forms and an embedding theorem for symplectic manifolds,” J. Differential Geom.,12, 229–235 (1977).zbMATHGoogle Scholar
  3. 3.
    Thurston W., “Some simple examples of compact symplectic manifolds,” Proc. Amer. Math. Soc.,55, 467–468 (1976).zbMATHCrossRefGoogle Scholar
  4. 4.
    McDuff D., “Examples of symplectic simply connected manifolds with no Kähler structure,” J. Differential Geom.,20, 267–277 (1984).zbMATHGoogle Scholar
  5. 5.
    Gompf R. E., “A new construction of symplectic manifolds,” Ann. of Math. (2),142, 527–595 (1995).zbMATHCrossRefGoogle Scholar
  6. 6.
    Deligne P., Griffiths P., Morgan J., andSullivan D., “Real homotopy theory of Kähler manifolds,” Invent. Math.,19, 245–274 (1975).CrossRefGoogle Scholar
  7. 7.
    Benson C. andGordon C., “Kähler and symplectic structures on nilmanifolds,” Topology,27, 513–518 (1988).zbMATHCrossRefGoogle Scholar
  8. 8.
    Lupton G. andOprea J., “Symplectic Manifolds and formality,” J. Pure Appl. Algebra,91, 193–207 (1994).zbMATHCrossRefGoogle Scholar
  9. 9.
    Tralle A. andOprea J., Sympletic Manifolds with No Kähler Structure, Springer-Verlag, Berlin and Heidelberg (1997). (Lecture Notes in Math.;1661.)Google Scholar
  10. 10.
    Neisendorfer J. andMiller T., “Formal and coformal spaces,” Illinois J. Math.,22 565–579 (1978).zbMATHGoogle Scholar
  11. 11.
    Babenko I. K. andTaimanov I. A., “On existence of nonformal simply-connected symplectic manifolds,” Uspekhi Mat. Nauk,53, No. 5, 225–226 (1998).Google Scholar
  12. 12.
    Fernandez M., Gotay M., andGray A., “Compact parallelizable four dimensional symplectic and complex manifolds,” Proc. Amer. Math. Soc.,103, 1209–1212 (1988).zbMATHCrossRefGoogle Scholar
  13. 13.
    Husemoller D., Fibre Bundles, McGraw-Hill, New York (1996).Google Scholar
  14. 14.
    Gromov M. L., Partial Differential Relations, Springer-Verlag, Berlin and Heidelberg (1986).zbMATHGoogle Scholar
  15. 15.
    Sullivan J., “Infinitesimal computations in topology,” Publ. IHES,47, 269–331 (1978).Google Scholar
  16. 16.
    Griffiths P. andMorgan J., Rational Homotopy Theory and Differential Forms, Birkhäuser, Basel (1981).zbMATHGoogle Scholar
  17. 17.
    Malcev A. I., “On a class of homogeneous spaces,” Izv. Akad. Nauk SSSR Ser. Mat.,3, 9–32 (1949).Google Scholar
  18. 18.
    Nomizu K., “On the cohomology of homogeneous spaces of nilpotent Lie groups,” Ann. of Math. (2),59, 531–538 (1954).CrossRefGoogle Scholar
  19. 19.
    Thomas J. C., “Rational homotopy of Serre fibrations,” Ann. Inst. Fourier (Grenoble),31, No. 3, 71–90 (1981).zbMATHGoogle Scholar
  20. 20.
    Fuks D. B., Cohomology of Infinite-Dimensional Lie Algebras [in Russian], Nauka, Moscow (1984).zbMATHGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • I. K. Babenko
  • I. A. Taîmanov

There are no affiliations available

Personalised recommendations