, Volume 29, Issue 4, pp 311-328

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

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.