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2006•Canadian Journal of MathematicsOpen access

Cohomology Pairings on the Symplectic Reduction of Products

Rebecca Goldin, Shaun Martin

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Abstract

Abstract 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 × 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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Abstract 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 × 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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Available abstract

Abstract 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 × 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.

Key concepts: Mathematics, Symplectic geometry, Diagonal, Cohomology, Pure mathematics, Moment map, Product (mathematics), Convolution (computer science)

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