Letters in Mathematical Physics

, Volume 29, Issue 4, pp 311-328

First online:

An integration formula for the square of moment maps of circle actions

  • Siye WuAffiliated withDepartment of Mathematics, Columbia University

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The integration of the exponential of the square of the moment map of the circle action is studied by a direct stationary phase computation and by applying the Duistermaat-Heckman formula. Both methods yield two distinct formulas expressing the integral in terms of contributions from the critical set of the square of the moment map. Certain cohomological pairings on the symplectic quotient are computed explicitly using the asymptotic behavior of the two formulas.

Mathematics Subject Classifications (1991)

53C15 57R70 41A60 55N91