Inventiones mathematicae

, Volume 97, Issue 3, pp 485–522 | Cite as

Birational equivalence in the symplectic category

  • V. Guillemin
  • S. Sternberg
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A] Atiyah, M.: Convexity and commuting Hamiltonians. Bull. Lond. Math. Soc.14, 1–15 (1982)Google Scholar
  2. [D-H] Duistermaat, J.J., Heckman, G.: On the variation of cohomology of the symplectic form on the reduced phase space. Invent. Math.69, 259–268 (1982)Google Scholar
  3. [G] Gromov, M.: Pseudoholomorphic curves in symplectic manifolds. Invent. Math.82, 307–347 (1985)Google Scholar
  4. [G-N] Gotay, M., Nester, J.: Pre-symplectic manifolds and the Dirac-Bergmann theory of constraints. J. Math. Phys.19, 2388–2399 (1978)Google Scholar
  5. [G-S]1 Guillemin, V., Sternberg, S.: Convexity properties of the moment map. Invent. Math.67, 491–513 (1982)Google Scholar
  6. [G-S]2 Guillemin, V., Sternberg, S.: Geometric quantization and multiplicities of group representations. Invent. Math.67, 515–538 (1982)Google Scholar
  7. [G-S]3 Guillemin, V., Sternberg, S.: Symplectic Techniques in Physics. Cambridge Univ. Press 1984Google Scholar
  8. [H] Heckman, G.: Thesis. University of Leiden 1980Google Scholar
  9. [Hi] Hirzebruch, F.: The signature of ramified coverings. Lecture given at the Summer Institute on Global Analysis, AMS Berkeley, July, 1968. Symposium in honor of K. Kodaira, D.C. Spencer (ed.). AMS Pub. Providence, 1970Google Scholar
  10. [K-K-S] Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Commun. Pure Appl. Math.31, 481–508 (1978)Google Scholar
  11. [Kir] Kirwan, F.: Cohomology of quotients in symplectic and algebraic geometry. Princeton Univ. Press, Princeton, N.J. 1984Google Scholar
  12. [Kod] Kodaira, K.: Complex manifolds and deformations of complex structures. Berlin-Heidelberg-New York: Springer 1986Google Scholar
  13. [Kos] Kostant, D.: A formula for the multiplicity of a weight. Trans. Am. Math. Soc.93, 53–73 (1959)Google Scholar
  14. [M]1 MacDuff, D.: Examples of simply connected non-Kahlerian manifolds. J. Differ. Geom.20, 267–277 (1984)Google Scholar
  15. [M]2 MacDuff, D.: Examples of symplectic structures. Preprint, SUNY Stony Brook 1986Google Scholar
  16. [Mel] Melrose, R.: Analysis on manifolds with corners. MIT 1988Google Scholar
  17. [M-F] Mumford, D., Fogarty, J.: Geometric invariant theory. Berlin-Heidelberg-New York: Springer 1982Google Scholar
  18. [N] Ness, L.: A stratification of the null cone via the moment map. Am. J. Math.106, 1281–1325 (1984)Google Scholar
  19. [S] Sternberg, S.: On minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field., Proc. Natl. Acad. Sci. USA74, 5253–5254 (1977)Google Scholar
  20. [W]1 Weinstein, A.: Lectures on Symplectic manifolds. CBMS Reg. Conf. Ser. Math., Vol. 29. AMS Providence, R.I. 1977Google Scholar
  21. [W]2 Weinstein, A.: Fat bundles and symplectic manifolds. Adv. Math.37, 239–250 (1980)Google Scholar
  22. [Z] Zhelobenko, D.P.: Compact Lie groups and their representations. AMS Transl., Vol. 40. AMS, Providence, R.I. 1972Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • V. Guillemin
    • 1
  • S. Sternberg
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations