Smooth structures on certain moduli spaces for bundles on a surface

Journal of Pure and Applied Algebra

Volumn 126, Issue 1-3, 1998, Pages 183-221

  Huebschmann, Johannes ^a  

^a UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032037364     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(96)00133-8     Document Type: Article

References (36)

1. [1] R. Abraham and J.E. Marsden, Foundations of Mechanics (Benjamin/Cummings, Menlo Park, CA, 1978).
2. [2] J.M. Arms, M.J. Gotay and G. Jennings, Geometric and algebraic reduction for singular momentum mappings, Adv. Math. 79 (1990) 43-103.
3. [3] J.M. Arms, J.E. Marsden and V. Moncrief, Symmetry and bifurcation of moment mappings, Comm. Math. Phys. 78 (1981) 455-478.
4. [4] M. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London A 308 (1982) 523-615.
5. [5] J. Bochnak, M. Coste and M.-F. Roy, Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 12. A series of modern surveys in Mathematics, Vol. 12 (Springer, Berlin, 1987).
6. [6] D. Ebin, The manifold of Riemannian metrics, Proc. Symp. Pure Mathematics, Vol. 15 (Amer. Math. Soc., Providence, RI, 1970) 11-40.
7. [7] J. Eells, A setting for global analysis, Bull. Amer. Math. Soc. 72 (1966) 751-807
8. [8] W.M. Goldman, The symplectic nature of the fundamental group of surfaces, Advances 54 (1984) 200-225.
9. [9] R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989) 539-570.
10. [10] J. Huebschmann, Holonomies of central Yang-Mills connections for bundles on a surface with disconnected structure group, Math. Proc. Camb. Phil. Soc. 116 (1994) 375-384.
11. [11] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. I. The local model, Math. Z. 220 (1995) 595-609.
12. [12] J. Huebschmann, Poisson structures on certain moduli spaces for bundles on a surface, Annales de l'Institut Fourier 45 (1995) 65-91.
13. [13] J. Huebschmann, Symplectic and Poisson structures of certain moduli spaces, Duke Math. J. 80 (1995) 737-756.
14. [14] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. II. The stratification, Math. Z. 221 (1996) 83-92.
15. [15] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. III. The identification of the strata, in preparation.
16. [16] J. Huebschmann, Poisson geometry of flat connections for SU(2)-bundles on surfaces, Math. Z. 221 (1996) 243-259.
17. [17] J. Huebschmann and L. Jeffrey, Group cohomology construction of symplectic forms on certain moduli spaces, Int. Math. Res. Notices 6 (1994) 245-249.
18. [18] S. Kobayashi and K. Nomizu, Foundations of differential geometry, I (1963), II (1969), Interscience Tracts in Pure and Applied Mathematics, No. 15 (Interscience Publ., New York, 1969).
19. [19] B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963) 327-404.
20. [20] E. Lerman, R. Montgomery and R. Sjamaar, Examples of singular reduction, symplectic geometry, in: Warwick, 1990, D.A. Salamon, Ed., London Math. Soc. Lecture Note Series, Vol. 192 (Cambridge Univ. Press, Cambridge, 1993) 127-155.
21. [21] J. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetries, Rep. Math. Phys. 5 (1974) 121-130.
22. [22] J. Mather, Differentiable invariants, Topology 16 (1977) 145-155.
23. [23] P.K. Mitter and C.M. Viallet, On the bundle of connections and the gauge orbit manifold in Yang-Mills theory, Comm. Math. Phys. 79 (1981) 457-472.
24. [24] M.S. Narasimhan and T.R. Ramadas, Geometry of SU(2)-gauge fields, Comm. Math. Phys. 67 (1979) 121-136.
25. [25] M.S. Narasimhan and S. Ramanan, Moduli of vector bundles on a compact Riemann surface, Ann. Math. 89 (1969) 19-51.
26. [26] M.S. Narasimhan and C.S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. Math. 82 (1965) 540-567.
27. [27] M.S. Raghunatan, Discrete Subgroups of Lie Groups (Springer, Berlin, 1972).
28. [28] G.W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975) 63-68.
29. [29] G.W. Schwarz, The topology of algebraic quotients, in: Topological methods in algebraic transformation groups, Progress in Math., Vol. 80 (Birkhäuser, Basel 1989) 135-152.
30. [30] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. Math. 134 (1991) 375-422.
31. [31] A. Weil, On discrete subgroups of Lie groups, (a) Ann. Math. 72 (1960) 369-384;
32. (b) Ann. Math. 75 (1962) 578-602.
33. [32] A. Weil, Remarks on the cohomology of groups, Ann. Math. 80 (1964) 149-157.
34. [33] H. Weyl, The Classical Groups (Princeton Univ. Press, Princeton, NJ, 1946).
35. [34] H. Whitney, Analytic extensions of differentiable functions defined on closed sets, Trans. Amer. Math. Soc. 36 (1934) 63-89.
36. [35] H. Whitney, Elementary structure of real algebraic varieties, Ann. Math. 66 (1957) 545-556.