On the localization theorem in equivariant cohomology

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We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties.
8 pages, Latex2e, uses epsfig

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