Cohomology Pairings on the Symplectic Reduction of Products

http://dx.doi.org/10.4153/CJM-2006-015-3
Canad. J. Math. 58(2006), 362-380

  Published:2006-04-01
 Printed: Apr 2006

Let $M$ be the product of two compact Hamiltonian $T$-spaces $X$ and $Y$. We present a formula for evaluating integrals on the symplectic reduction of $M$ by the diagonal $T$ action. At every regular value of the moment map for $X\times Y$, the integral is the convolution of two distributions associated to the symplectic reductions of $X$ by $T$ and of $Y$ by $T$. Several examples illustrate the computational strength of this relationship. We also prove a linear analogue which can be used to find cohomology pairings on toric orbifolds.