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Extended moduli spaces of flat connections on Riemann surfaces

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References

  1. Audin, M.: The topology of torus actions on symplectic manifolds (Prog. Math., vol. 93) Boston Basel Stuttgart: Birkhäuser 1991

    Google Scholar 

  2. Atiyah, M.F., Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond.A308, 523–615 (1982)

    Google Scholar 

  3. Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry I. Math. Proc. Camb. Philos. Soc.77, 43–67 (1975)

    Google Scholar 

  4. Bauer, S.: Parabolic bundles, elliptic surfaces and SU(2)-representation spaces of genus zero Fuchsian groups. Math. Ann.290, 509–526 (1991)

    Google Scholar 

  5. Cappell, S., Lee, R., Miller, E.: Self adjoint elliptic operators and manifold decomposition, Part I: Low eigenmodes and stretching. (Preprint 1992)

  6. Chang, S.: Non-abelian theta functions, geometric quantization and a mathematical proof of Verlinde's formula. (Preprint 1992)

  7. Daskalopoulos G., Wentworth, R.: Geometric quantization for the moduli space of vector bundles with parabolic structure. (Preprint 1991)

  8. Donaldson S.K.: Gluing techniques in the cohomology of moduli spaces. In: Hofer, H., Taubes, C.H., Zehnder, E. (eds.) The Memorial volume to Andreas Floer. (to appear 1992)

  9. Donaldson, S.K., Furuta, M.: Floer homology groups in Yang-Mills theory. (to appear 1992)

  10. Donaldson, S.K., Kronheimer, P.: The geometry of four-manifolds. Oxford: Oxford University Press 1990

    Google Scholar 

  11. Freed, D., Uhlenbeck, K.: Instantons and four-manifolds, second edn. (Publ. Math. Sci. Res. Inst., vol. 1) Berlin Heidelberg New York: Springer 1991

    Google Scholar 

  12. Goldman, W.: The symplectic nature of fundamental groups of surfaces. Adv. Math.54, 200–225 (1984)

    Google Scholar 

  13. Goldman, W.: Invariant functions on Lie groups and Hamiltonian flows of surface group representations. Invent. Math.85, 263 (1986)

    Google Scholar 

  14. Guillemin, V., Sternberg, S.: Convexity properties of the moment map. Invent. Math.67, 491–513 (1982)

    Google Scholar 

  15. Guillemin, V., Sternberg, S.: Birational equivalence in the symplectic category. Invent. Math.97, 485–522 (1989)

    Google Scholar 

  16. Guillemin, V., Sternberg, S.: Symplectic techniques in physics. Cambridge: Cambridge University Press 1984

    Google Scholar 

  17. Guillemin, V., Lerman, E., Sternberg, S.: Symplectic fibrations and multiplicity diagrams. (to appear 1992)

  18. Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York London: Academic Press 1978

    Google Scholar 

  19. Huybrechts, D., Lehn, M.: Stable pairs on curves and surfaces. Preprint alg-geom/9211001 (1992); J. Algebraic Geom. (to appear)

  20. Jeffrey, L.C., Kirwan, F.C.: Localization for nonabelian group actions. Preprint alg-geom/9307001 (1993)

  21. Jeffrey, L., Weitsman, J.: Toric structures on the moduli space of flat connections on a Riemann surface: volumes and the moment map. Adv. Math. (to appear)

  22. Jeffrey, L., Weitsman, J.: In preparation

  23. Lockhart, R.B., McOwen, R.C.: Elliptic differential operators on noncompact manifolds. Ann. Sc. Norm. Super. Pisa14, 409–447 (1985)

    Google Scholar 

  24. Matic, G.: SO(3)-connections and rational homology cobordisms. J. Differ. Geom.28, 277–307 (1988)

    Google Scholar 

  25. Mehta, V., Seshadri, C.S.: Moduli of vector bundles on curves with parabolic structures. Math. Ann.248, 205–239 (1980)

    Google Scholar 

  26. Seshadri, C.S., Fibrés vectoriels sur les courbes algébriques. Astérisque96 (1982)

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

    Google Scholar 

  28. Taubes, C.H.: Gauge theory on asymptotically periodic 4-manifolds. J. Differ. Geom.25, 361–430 (1987)

    Google Scholar 

  29. Thaddeus, M.: Stable pairs, linear systems and the Verlinde formula. Math. Sci. Res. Inst. Preprint alg-geom/9210007 (1992); Invent. Math. (in press 1994)

  30. Witten, E.: On quantum gauge theories in two dimensions. Commun. Math. Phys.141, 153–209 (1991)

    Google Scholar 

  31. Witten, E.: Two dimensional gauge theories revisited. Preprint hep-th/9204083 (1992); J. Geom. Phys.9, 303–368 (1992)

    Google Scholar 

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Authors and Affiliations

  1. Downing College, CB2 1DQ, Cambridge, UK

    Lisa C. Jeffrey

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  1. Lisa C. Jeffrey
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Supported in part by a grant in aid from the J. Seward Johnson Charitable Trust

Address after 1 September 1993: Mathematics Department, Princeton University, Princeton, NJ 08544, USA

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Jeffrey, L.C. Extended moduli spaces of flat connections on Riemann surfaces. Math. Ann. 298, 667–692 (1994). https://doi.org/10.1007/BF01459756

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  • DOI: https://doi.org/10.1007/BF01459756

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