Mathematische Zeitschrift

, Volume 221, Issue 1, pp 243–259 | Cite as

Poisson geometry of flat connections for SU(2)-bundles on surfaces

  • Johannes Huebschmann
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Keywords

Modulus Space Poisson Bracket Poisson Structure Symplectic Structure Momentum Mapping 
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References

  1. 1.
    J. M. Arms, R. Cushman, and M. J. Gotay: A universal reduction procedure for Hamiltonian group actions, in: The geometry of Hamiltonian systems, T. Ratiu, ed. MSRI Publ. Vol. 20, pp. 33–51. Berlin-Heidelberg-New York-Tokyo: Springer 1991Google Scholar
  2. 2.
    M. Atiyah and R. Bott: The Yang-Mills equations over Riemann surfaces. Phil. Trans. R. Soc. London A 308: 523–615 (1982)MathSciNetGoogle Scholar
  3. 3.
    M. J. Gotay and L. Bos: Singular angular momentum mappings. J. Diff. Geom. 24: 181–203 (1986)MATHMathSciNetGoogle Scholar
  4. 4.
    J. Huebschmann: Poisson cohomology and quantization. J. für die Reine und Angewandte Mathematik 408: 57–113 (1990)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    J. Huebschmann: On the quantization of Poisson algebras, in: Symplectic Geometry and Mathematical Physics, Actes du colloque en l’honneur de Jean-Marie Souriau, P. Donato, C. Duval, J. Elhadad, G.M. Tuynman, eds.; Progress in Mathematics, Vol. 99, pp. 204–233. Boston · Basel · Berlin: Birkhäuser 1991Google Scholar
  6. 6.
    J. Huebschmann The singularities of Yang-Mills connections for bundles on a surface. I. The local model Math. Z. (to appear), dg-ga/9411006Google Scholar
  7. 7.
    J. Huebschmann: The singularities of Yang-Mills connections for bundles on a surface. II. The stratification. Math. Z. (to appear), dg-ga/9411007Google Scholar
  8. 8.
    J. Huebschmann: Holonomies of Yang-Mills connections for bundles on a surface with disconnected structure group. Math. Proc. Camb. Phil. Soc. 116: 375–384 (1994)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    J. Huebschmann: Smooth structures on certain moduli spaces for bundles on a surface. Preprint 1992, dg-ga/9411008Google Scholar
  10. 10.
    J. Huebschmann: Poisson structures on certain moduli spaces for bundles on a surface Annales de l’Institut Fourier 45: 65–91 (1995)MATHMathSciNetGoogle Scholar
  11. 11.
    J. Huebschmann: Symplectic and Poisson structures of certain moduli spaces. Duke Math. J. (to appear), hep-th/9312112Google Scholar
  12. 12.
    J. Huebschmann: Symplectic and Poisson structures of certain moduli spaces. II. Projective representationx of cocompact planar discrete groups. Duke Math. J. (to appear), dg-ga/9412003Google Scholar
  13. 13.
    J. Huebschmann and L. Jeffrey: Group cohomology construction of symplectic forms on certain moduli spaces. Int. Math. Research Notices 6: 245–249 (1994)CrossRefMathSciNetGoogle Scholar
  14. 14.
    G. Kempf and L. Ness: The length of vectors in representation spaces. Lecture Notes in Mathematics. Vol. 732: Algebraic geometry, Copenhagen, 1978, pp. 233–244. Berlin-Heidelberg-New York: Springer 1978Google Scholar
  15. 15.
    E. Lerman, R. Montgomery and R. Sjamaar: Examples of singular reduction. In: Symplectic Geometry. Warwick, 1990, ed. D. A. Salamon, London Math. Soc. Lecture Note Series Vol. 192, pp. 127–155. Cambridge, UK: Cambridge University Press 1993Google Scholar
  16. 16.
    M. S. Narasimhan and S. Ramanan: Moduli of vector bundles on a compact Riemann surface. Ann. of Math. 89: 19–51 (1969)CrossRefMathSciNetGoogle Scholar
  17. 17.
    M. S. Narasimhan and S. Ramanan: 2ϑ-linear systems on abelian varieties. Bombay colloquium. pp. 415–427 (1985)Google Scholar
  18. 18.
    G. W. Schwarz: The topology of algebraic quotients, in: Topological methods in algebraic transformation groups. Progress in Math. vol 80: 135–152, Boston Basel Berlin: Birkhäuser 1989Google Scholar
  19. 19.
    C. S. Seshadri: Spaces of unitary vector bundles on a compact Riemann surface. Ann. of Math. 85: 303–336 (1967)CrossRefMathSciNetGoogle Scholar
  20. 20.
    C. S. Seshadri: Fibrés vectoriels sur les courbes algébriques. Astérisque Vol. 96. Soc. Math. de France 1982Google Scholar
  21. 21.
    R. Sjamaar and E. Lerman: Stratified symplectic spces and reduction. Ann. of Math. 134: 375–422 (1991)CrossRefMathSciNetGoogle Scholar
  22. 22.
    H. Weyl: The classical groups. Princeton NJ: Princeton University Press 1946MATHGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Johannes Huebschmann
    • 1
  1. 1.Max Planck Institut für MathematikBonnGermany

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