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

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Raoul Bott: Collected Papers

Part of the book series: Contemporary Mathematicians ((CM))

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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.

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Notes

  1. 1.

    We omit details about smoothness of loops in this brief introduction; see (BTW) for details.

  2. 2.

    Although the Morse theory goes through in both cases (B; D).

  3. 3.

    This means that we get an honest equivariant action of the central extension.

  4. 4.

    To obtain a smooth quotient, take the moment map Φ −I. 

  5. 5.

    Recall that since ΩG acts freely on X, X∕∕LG = μ −1(0)∕G. 

References

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Jonathan Weitsman

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  1. Jonathan Weitsman
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Correspondence to Jonathan Weitsman .

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Editors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, USA

    Loring W. Tu

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Weitsman, J. (2017). Commentary on “Surjectivity for Hamiltonian Loop Group Spaces” [120]. In: Tu, L. (eds) Raoul Bott: Collected Papers . Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51781-0_16

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