Canadian Mathematical Society
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Cohomology Pairings on the Symplectic Reduction of Products

 Printed: Apr 2006
  • R. F. Goldin
  • S. Martin
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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.
MSC Classifications: 53D20 show english descriptions Momentum maps; symplectic reduction 53D20 - Momentum maps; symplectic reduction

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