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Commentary on “Surjectivity for Hamiltonian Loop Group Spaces” [120]

  • Jonathan Weitsman
Chapter
Part of the Contemporary Mathematicians book series (CM)

Abstract

Two of Raoul Bott’s major works (B; AB) study Morse theory in two apparently unrelated settings. In (BTW), we show that these results fit into a general theorem about Hamiltonian actions of loop groups.

References

  1. [AMM]
    A. Alexeev, A. Malkin, and E. Meinrenken, Lie group valued moment maps. J. Diff. Geom. 48 445–495 (1998)Google Scholar
  2. [AB]
    M. Atiyah, R. Bott. The Yang-Mills functional over a Riemann surface. Phil. Trans. Roy. Soc. A308, 523–615 (1982)Google Scholar
  3. [B]
    R. Bott, The stable homotopy of the classical groups. Ann. Math. 70, 313–337 (1957)Google Scholar
  4. [BTW]
    R. Bott, S. Tolman, J. Weitsman. Surjectivity for Hamiltonian Loop Group Spaces. Inv. Math. 155, 225–251 (2004)Google Scholar
  5. [D]
    Daskalopoulos, Georgios D. The topology of the space of stable bundles on a compact Riemann surface. J. Differential Geom. 36 (1992), no. 3, 699–746.Google Scholar
  6. [K]
    F. C. Kirwan, The cohomology of quotients in symplectic and algebraic geometry, Princeton University Press, 1984.Google Scholar
  7. [N]
    Newstead, P. E. Topological properties of some spaces of stable bundles. Topology 6 (1967) 241–262.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA

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