Cohomology Pairings on the Symplectic Reduction of Products
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.
53D20 - Momentum maps; symplectic reduction