Skip to main content
SpringerLink
Log in

The singularities of Yang-Mills connections for bundles on a surface

I. The local model

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Abraham, R., Marsden, J.E.: Foundations of Mechanics, Benjamin-Cummings Publishing Company, 1978

  2. Arms, J.M., Gotay, M.J., Jennings, G.: Geometric and algebraic reduction for singular momentum mappings, Advances in Mathematics79 (1990), 43–103

    Article  MATH  MathSciNet  Google Scholar 

  3. Arms, J.M., Marsden, J.E., Moncrief, V.: Symmetry and bifurcation of moment mappings, Comm. Math. Phys.78 (1981), 455–478

    Article  MATH  MathSciNet  Google Scholar 

  4. Atiyah, M., Bott, R.: The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London A308 (1982), 523–615

    MathSciNet  Google Scholar 

  5. Ebin, D.: The manifold of Riemannian metrics, Proceedings of symposia in Pure Mathematics15 (1970), American Math. Soc., Providence, R. I, 11–40

    Google Scholar 

  6. Goldman, W.M., Millson, J.: Differential graded Lie algebras and singularities of level set momentum mappings. Commun. Math. Phys.131 (1990), 495–515

    Article  MATH  MathSciNet  Google Scholar 

  7. Huebschmann, J.: The singularities of Yang-Mills connections for bundles on a surface. II. The stratification Math. Z. (to appear)

  8. Huebschmann, J.: The singularities of Yang-Mills connections for bundles on a surface. III. The identification of the strata, info in preparation

  9. Huebschmann, J.: Holonomies of Yang-Mills connections for bundles on a surface with disconnected structure group, Math. Proc. Cambr. Phil. Soc.116 (1994), 375–384

    Article  MATH  MathSciNet  Google Scholar 

  10. Huebschmann, J.: Smooth structures on certain moduli spaces for bundles on a surface, preprint 1992

  11. Huebschmann, J.: Poisson structures on certain moduli spaces for bundles on a surface, Ann. Inst. Fourier45 (1995), 65–91

    MATH  MathSciNet  Google Scholar 

  12. Huebschmann, J.: Poisson geometry of flat connections for SU(2)-bundles on surfaces, Math. Z. (to appear)

  13. Huebschmann, J.: Symplectic and Poisson structures of certain moduli spaces, Duke Math. (to appear)

  14. Huebschmann, J., Jeffrey, L.: Group cohomology construction of symplectic forms on certain moduli spaces, Int. Math. Research Notices 1994, No. 6, 245–249

    Article  MathSciNet  Google Scholar 

  15. Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetries, Rep. on Math. Phys.5 (1974), 121–130

    Article  MATH  MathSciNet  Google Scholar 

  16. Mitter, P.K., Viallet, C.M.: On the bundle of connections and the gauge orbit manifold in Yang-Mills theory, Comm. in Math. Phys.79 (1981), 457–472

    Article  MATH  MathSciNet  Google Scholar 

  17. Narasimhan M.S., Ramadas, T.R.: Geometry of SU(2)-gauge fields, Comm. in Math. Phys.67 (1979), 121–136

    Article  MATH  MathSciNet  Google Scholar 

  18. Narasimhan M.S., Seshadri, C.S.: Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math.82 (1965), 540–567

    Article  MathSciNet  Google Scholar 

  19. Singer, I.M.: Some remarks about the Gribov ambiguity, Comm. in Math. Phys.60 (1978), 7–12

    Article  MATH  Google Scholar 

  20. Sjamaar, R.: Singular orbit spaces in Riemannian and Symplectic geometry, Thesis, University of Utrecht, 1990

  21. Sjamaar R., Lerman, E.: Stratified symplectic spaces and reduction, Ann. of Math.134 (1991) 375–422

    Article  MathSciNet  Google Scholar 

  22. Weinstein, A.: On the symplectic structure of moduli space, A. Floer memorial (to appear)

Download references

Author information

Authors and Affiliations

  1. U. F. R. de Mathématiques, Université des Sciences et Technologie de Lille, F-59 655, VILLENEUVE D'ASCQ, France

    Johannes Huebschmann

Authors
  1. Johannes Huebschmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author carried out this work in the framework of the VBAC research group of Europroj.

Address from September 1,1994: Max Planck Institut für Mathematik, Gottfried Claren-Strasse 26, D-53 225 Bonn, Germany

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huebschmann, J. The singularities of Yang-Mills connections for bundles on a surface. Math Z 220, 595–609 (1995). https://doi.org/10.1007/BF02572633

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02572633

Keywords

Search

Navigation