Cohomology Pairings on the Symplectic Reduction of Products

Goldin, R. F. ; Martin, S.

Canadian journal of mathematics, Tome 58 (2006) no. 2, pp. 362-380

Résumé

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.

Détail

DOI : 10.4153/CJM-2006-015-3

Mots-clés : 53D20

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