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Cohomology Pairings on the Symplectic Reduction of Products

Published online by Cambridge University Press:  20 November 2018

R. F. Goldin  and
S. Martin
R. F. Goldin
Affiliation:
George Mason University, MS3 F2, 4400 University Drive, Fairfax, Virginia 22030, USA e-mail: rgoldin@math.gmu.edu e-mail: shaun@mindwasabi.com
S. Martin
Affiliation:
George Mason University, MS3 F2, 4400 University Drive, Fairfax, Virginia 22030, USA e-mail: rgoldin@math.gmu.edu e-mail: shaun@mindwasabi.com
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Abstract

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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.

Keywords

53D20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 2 , 01 April 2006 , pp. 362 - 380
Copyright
Copyright © Canadian Mathematical Society 2006

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