Duke Mathematical Journal

Group systems, groupoids, and moduli spaces of parabolic bundles

K. Guruprasad, J. Huebschmann, L. Jeffrey, and A. Weinstein

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 89, Number 2 (1997), 377-412.

Dates
First available: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077241022

Mathematical Reviews number (MathSciNet)
MR1460627

Zentralblatt MATH identifier
0885.58011

Digital Object Identifier
doi:10.1215/S0012-7094-97-08917-1

Subjects
Primary: 58D29: Moduli problems for topological structures
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 58F05

Citation

Guruprasad, K.; Huebschmann, J.; Jeffrey, L.; Weinstein, A. Group systems, groupoids, and moduli spaces of parabolic bundles. Duke Mathematical Journal 89 (1997), no. 2, 377--412. doi:10.1215/S0012-7094-97-08917-1. http://projecteuclid.org/euclid.dmj/1077241022.


Export citation

References

  • [1] M. Atiyah, The geometry and physics of knots, Lezioni Lincee. [Lincei Lectures], Cambridge University Press, Cambridge, 1990.
  • [2] M. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523–615.
  • [3] R. Bieri and B. Eckmann, Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra 13 (1978), no. 3, 277–319.
  • [4] I. Biswas and K. Guruprasad, Principal bundles on open surfaces and invariant functions on Lie groups, Internat. J. Math. 4 (1993), no. 4, 535–544.
  • [5] I. Biswas and K. Guruprasad, On some geometric invariants associated to the space of flat connections on an open space, Canad. Math. Bull. 39 (1996), no. 2, 169–177.
  • [6] R. Bott, On the Chern-Weil homomorphism and the continuous cohomology of Lie-groups, Advances in Math. 11 (1973), 289–303.
  • [7] R. Bott, H. Shulman, and J. Stasheff, On the de Rham theory of certain classifying spaces, Advances in Math. 20 (1976), no. 1, 43–56.
  • [8] R. Brown, Elements of Modern Topology, McGraw-Hill Book Co., New York, 1968.
  • [9] S. Eilenberg and S. MacLane, Relations between homology and homotopy groups of spaces, Ann. of Math. (2) 46 (1945), 480–509.
  • [10] V. V. Fock and A. A. Rosly, Flat connections and polyubles, Teoret. Mat. Fiz. 95 (1993), no. 2, 228–238.
  • [11] W. M. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984), no. 2, 200–225.
  • [12] K. Guruprasad, Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces, Pacific J. Math. 162 (1994), no. 1, 45–55.
  • [13] K. Guruprasad and C. S. Rajan, Group cohomology and the symplectic structure on the moduli space of representations, preprint, McGill Univ., 1995.
  • [14] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978.
  • [15] J. Huebschmann, Symplectic and Poisson structures of certain moduli spaces. I, Duke Math. J. 80 (1995), no. 3, 737–756.
  • [16] J. Huebschmann, Symplectic and Poisson structures of certain moduli spaces. II. Projective representations of cocompact planar discrete groups, Duke Math. J. 80 (1995), no. 3, 757–770.
  • [17] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. I. The local model, Math. Z. 220 (1995), no. 4, 595–609.
  • [18] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. II. The stratification, Math. Z. 221 (1996), no. 1, 83–92.
  • [19] J. Huebschmann, Smooth structures on moduli spaces of central Yang-Mills connections for bundles on a surface, to appear in J. Pure Appl. Alg.; dg-ga/9411008.
  • [20] J. Huebschmann, Poisson structures on certain moduli spaces for bundles on a surface, Ann. Inst. Fourier (Grenoble) 45 (1995), no. 1, 65–91.
  • [21] J. Huebschmann, Poisson geometry of flat connections for $\rm SU(2)$-bundles on surfaces, Math. Z. 221 (1996), no. 2, 243–259.
  • [22] J. Huebschmann, Poisson geometry of certain moduli spaces, Rend. Circ. Mat. Palermo (2) Suppl. (1996), no. 39, 15–35, The Proceedings of the Winter School “Geometry and Physics” (Srni, 1994).
  • [23] J. Huebschmann and L. Jeffrey, Group cohomology construction of symplectic forms on certain moduli spaces, Internat. Math. Res. Notices (1994), no. 6, 245 ff., approx. 5 pp. (electronic).
  • [24] L. Jeffrey, Extended moduli spaces of flat connections on Riemann surfaces, Math. Ann. 298 (1994), no. 4, 667–692.
  • [25] L. Jeffrey, Symplectic forms on moduli spaces of flat connections on $2$-manifolds, Geometric topology (Athens, GA, 1993) ed. W. Kazez, AMS/IP Stud. Adv. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1997, Georgia International Topology Conference, pp. 268–281.
  • [26] L. Jeffrey, Group cohomology construction of the cohomology of moduli spaces of flat connections on $2$-manifolds, Duke Math. J. 77 (1995), no. 2, 407–429.
  • [27] Y. Karshon, An algebraic proof for the symplectic structure of moduli space, Proc. Amer. Math. Soc. 116 (1992), no. 3, 591–605.
  • [28] S. MacLane, Homology, Die Grundlehren der mathematischen Wissenschaften, Bd. 114, Academic Press Inc., Publishers, New York, 1963.
  • [29] M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567.
  • [30] H. B. Shulman, Characteristic classes and foliations, Ph.D. thesis, University of California, 1972.
  • [31] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. (2) 134 (1991), no. 2, 375–422.
  • [32] H. F. Trotter, Homology of group systems with applications to knot theory, Ann. of Math. (2) 76 (1962), 464–498.
  • [33] A. Weil, Remarks on the cohomology of groups, Ann. of Math. (2) 80 (1964), 149–157.
  • [34] A. Weinstein, The symplectic structure on moduli space, The Floer memorial volume ed. H. Hofer, et al., Progr. Math., vol. 133, Birkhäuser, Basel, 1995, pp. 627–635.