Poisson structures on certain moduli spaces for bundles on a surface
Annales de l'institut Fourier (1995)
- Volume: 45, Issue: 1, page 65-91
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topReferences
top- [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., 20 (1991), Springer Berlin-Heidelberg-New York-Tokyo, 33-51. Zbl0742.58016MR92h:58059
- [2] M. ATIYAH and R. BOTT, The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London, A 308 (1982), 523-615. Zbl0509.14014MR85k:14006
- [3] W. M. GOLDMAN, The symplectic nature of the fundamental groups of surfaces, Advances in Math., 54 (1984), 200-225. Zbl0574.32032MR86i:32042
- [4] W. M. GOLDMAN, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Inventiones Math., 85 (1986), 263-302. Zbl0619.58021MR87j:32069
- [5] J. HUEBSCHMANN, Poisson cohomology and quantization, J. für die Reine und Angewandte Mathematik, 408 (1990), 57-113. Zbl0699.53037MR92e:17027
- [6] J. HUEBSCHMANN, On the quantization of Poisson algebras, 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, Birkhäuser, Boston Basel Berlin, (1991), 204-233. Zbl0752.58012MR93g:58051
- [7] J. HUEBSCHMANN, The singularities of Yang-Mills connections for bundles on a surface. I. The local model, Math. Z. (to appear). Zbl0844.58011
- [8] J. HUEBSCHMANN, The singularities of Yang-Mills connections for bundles on a surface II. The stratification, Math. Z. (to appear). Zbl0844.58011
- [9] J. HUEBSCHMANN, Holonomies of Yang-Mills connections for bundles on a surface with disconnected structure group, Math. Proc. Cambr. Phil. Soc, 116 (1994), 375-384. Zbl0843.58013MR95f:58020
- [10] J. HUEBSCHMANN, Smooth structures on certain moduli spaces for bundles on a surface, preprint 1992. Zbl0918.58011
- [11] J. HUEBSCHMANN, The singularities of Yang-Mills connections for bundles on a surface. III. The identification of the strata, in preparation. Zbl0844.58011
- [12] J. HUEBSCHMANN, Poisson geometry of flat connections for SU(2)-bundles on surfaces, Math. Z. (to appear). Zbl0844.58014
- [13] J. HUEBSCHMANN, Symplectic and Poisson structures of certain moduli spaces, Duke Math. (to appear). Zbl0852.58037
- [14] J. HUEBSCHMANN and L. JEFFREY, Group cohomology construction of symplectic forms on certain moduli spaces, Int. Math. Research Notices, 6 (1994), 245-249. Zbl0816.58017MR95e:58033
- [15] Y. KARSHON, An algebraic proof for the symplectic structure of moduli space, Proc. Amer. Math. Soc., 116 (1992), 591-605. Zbl0790.14012MR93a:14010
- [16] J. MARSDEN and A. WEINSTEIN, Reduction of symplectic manifolds with symmetries, Rep. on Math. Phys., 5 (1974), 121-130. Zbl0327.58005MR53 #6633
- [17] M. S. NARASIMHAN and C. S. SESHADRI, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-567. Zbl0171.04803MR32 #1725
- [18] M. S. NARASIMHAN and S. RAMANAN, Moduli of vector bundles on a compact Riemann surface, Ann. of Math., 89 (1969), 19-51. Zbl0186.54902MR39 #3518
- [19] M. S. NARASIMHAN and S. RAMANAN, 2θ-linear systems on abelian varieties, Bombay Colloquium, (1985), 415-427. Zbl0685.14023MR88j:14014
- [20] C. S. SESHADRI, Spaces of unitary vector bundles on a compact Riemann surface, Ann. of Math., 85 (1967), 303-336. Zbl0173.23001MR38 #1693
- [21] R. SJAMAAR and E. LERMAN, Stratified symplectic spaces and reduction, Ann. of Math., 134 (1991), 375-422. Zbl0759.58019MR92g:58036
- [22] A. WEINSTEIN, On the symplectic structure of moduli space, A. Floer memorial, Birkhäuser Verlag, to appear. Zbl0834.58011
- [23] H. WHITNEY, Analytic extensions of differentiable functions defined on closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89. Zbl0008.24902MR1501735JFM60.0217.01