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Cobordism for Hamiltonian loop group actions and flat connections on the punctured two-sphere

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Abstract.

We develop a theory of symplectic cobordism and a Duistermaat-Heckman principle for Hamiltonian loop group actions. As an application, we construct a symplectic cobordism between moduli spaces of flat connections on the three holed sphere and disjoint unions of toric varieties. This cobordism yields formulas for the mixed Pontrjagin numbers of the moduli spaces, equivalent to Witten's formulas in the case of symplectic volumes.

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Authors and Affiliations

  1. University of Toronto, 100 St. George Street, Toronto, Ontario M5R 3G3, Canada (e-mail: mein@math.toronto.edu) , , , , , , CA

    E. Meinrenken

  2. Mathematics-Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA (e-mail: ctw@math.rutgers.edu) , , , , , , US

    C. Woodward

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  1. E. Meinrenken
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  2. C. Woodward
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Received June 15, 1998

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Meinrenken, E., Woodward, C. Cobordism for Hamiltonian loop group actions and flat connections on the punctured two-sphere. Math Z 231, 133–168 (1999). https://doi.org/10.1007/PL00004718

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  • DOI: https://doi.org/10.1007/PL00004718

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