Cohomology pairings on the symplectic reduction of products

Details Cohomology pairings on the symplectic reduction of products Cohomology pairings on the symplectic reduction of products

2004-08-18

arxiv.org/abs/math/0408250v1

Canad. J. Math. 58 (2006), no. 2, 362--380.

Mathematics

Symplectic Geometry

Accepted for publication in the Canadian Journal of Mathematics

Scientific paper

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 x 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.

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