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The geometry and topology of moduli spaces

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Global Geometry and Mathematical Physics

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References

  1. S. Amari, "Differential geometric methods in statistics", Lecture Notes in Statistics 28, Springer Verlag, Heidelberg (1985).

    Book  MATH  Google Scholar 

  2. M.F. Atiyah, "Geometry of Yang-Mills fields", Lez. Fermi Acc. Naz. dei Lincei of Scuola Norm. Sup., Pisa (1979).

    MATH  Google Scholar 

  3. M.F. Atiyah, "Instantons in two and four dimensions", Commun. Math. Phys. 93 (1984), 437–451.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  5. M.F. Atiyah & N.J. Hitchin, "The geometry and dynamics of magnetic monopoles", Rrinceton Univ. Press, Princeton (1988).

    Book  MATH  Google Scholar 

  6. M.F. Atiyah, N.J. Hitchin & I.M. Singer, "Self-duality in four-dimensional Riemannian geometry", Proc. Roy. Soc. Lond. A362 (1978) 425–461.

    Article  MathSciNet  MATH  Google Scholar 

  7. M.F. Atiyah, V.G. Drinfeld, N.J. Hitchin & Yu. I. Manin, "Construction of instantons", Phys. Lett. 65A (1978) 18 185–187.

    Article  MathSciNet  MATH  Google Scholar 

  8. N.P. Buchdahl, "Instantons on ℙP2", Commun. Math. Phys. 24 (1986) 19–52.

    MathSciNet  MATH  Google Scholar 

  9. S.K. Donaldson, "Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles", Proc. London Math. Soc. 50 (1985), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  10. S.K. Donaldson, "Vector bundles on the flag manifold and the Ward correspondence", in "Geometry of Today", eds. E. Arbarello, C. Procesi, E. Strickland, Birkhauser, Boston (1985) 109–119.

    Google Scholar 

  11. S.K. Donaldson, "Infinite determinants, stable bundles and curvature", Duke Math. J. 54 (1987) 231–247.

    Article  MathSciNet  MATH  Google Scholar 

  12. S.K. Donaldson, "Harmonic maps and the self-duality equations", Proc. London Math. Soc. 55 (1987) 127–132.

    Article  MathSciNet  MATH  Google Scholar 

  13. S.K. Donaldson, "Polynomial invariants for smooth four-manifolds", preprint Oxford (1988).

    Google Scholar 

  14. H. Doi, Y. Matsumoto & T. Matumoto, "An explicit formula of the metric on the moduli space of BPST-instantons over S4", "A Fête of Topology", Academic Press (1987).

    Google Scholar 

  15. C.J. Earle & J. Eells, "A fibre bundle description of Teichmüller theory", J. Diff. Geom. 3 (1969) 19–43.

    MathSciNet  MATH  Google Scholar 

  16. D.S. Freed & K.K. Uhlenbeck, "Instantons and four-manifolds", Springer Verlag, New York (1984).

    Book  MATH  Google Scholar 

  17. G. Gibbons & C. Pope, "The positive action conjecture and asymptotically Euclidean metrics in quantum gravity", Commun. Math. Phys. 66 (1979) 287–290.

    MathSciNet  Google Scholar 

  18. D. Groissier, "The geometry of the moduli space of â„™P2 instantons", preprint Stony Brook (1988).

    Google Scholar 

  19. D. Groissier & T.H. Parker, "The Riemannian geometry of the Yang-Mills moduli space", Commun. Math. Phys. 112 (1987) 663–689.

    Article  MathSciNet  MATH  Google Scholar 

  20. L. Habermann, "On the geometry of the space of Sp(1) instantons with Pontrjagin index 1 on the 4-sphere", Annals. of Global Analysis & Diff. Geom. (to appear).

    Google Scholar 

  21. N.J. Hitchin, "The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), 59–126.

    Article  MathSciNet  MATH  Google Scholar 

  22. N.J. Hitchin, A. Karlhede, U. Lindström & M. Rocek, "Hyperkähler metrics and supersymmetry", Commun. Math. Phys. 108 (1987) 535–589.

    Article  MATH  Google Scholar 

  23. A. Jaffe & C.H. Taubes, "Vortices and monopoles", Birkhauser, Boston (1980).

    MATH  Google Scholar 

  24. K. Kodaira, "Complex manifolds and deformation of complex structures", Springer Verlag, New York (1986).

    Book  MATH  Google Scholar 

  25. K. Kuranishi, "On the locally complete famlies of complex analytic structures", Annals of Math. 75 (1962), 536–477.

    Article  MathSciNet  MATH  Google Scholar 

  26. N.S. Manton, "Geometry of Skyrmions", Commun. Math. Phys. 111 (1987) 469–478.

    Article  MathSciNet  MATH  Google Scholar 

  27. V. Mathai & D. Quillen, "Superconnections, Thom classes and equivariant differential forms", Topology 25 (1986) 85–110.

    Article  MathSciNet  MATH  Google Scholar 

  28. D. Quillen, "Determinants of Cauchy-Riemann operators over a Riemann surface". Funct. Anal. Appl. 19 (1985) 31–34.

    Article  MathSciNet  MATH  Google Scholar 

  29. C.H. Taubes, "Stability in Yang-Mills theories", Commun. Math. Phys. 91 (1983) 235–263.

    Article  MathSciNet  MATH  Google Scholar 

  30. K. Uhlenbeck & S.T. Yau, "Hermitian-Einstein connections in stable vector bundles", Commun. Pure Appl. Math. Suppl. 39(S) (1986) 257–293.

    Article  MathSciNet  MATH  Google Scholar 

  31. E. Witten, "Topological quantum field thoery", Commun. Math. Phys. 117 (1988) 353–386.

    Article  MATH  Google Scholar 

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Mauro Francaviglia Francesco Gherardelli

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© 1990 Springer-Verlag

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Hitchin, N.J. (1990). The geometry and topology of moduli spaces. In: Francaviglia, M., Gherardelli, F. (eds) Global Geometry and Mathematical Physics. Lecture Notes in Mathematics, vol 1451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085064

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  • DOI: https://doi.org/10.1007/BFb0085064

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