Abstract
Using an idea of E. Witten (J. Geom. Phys. 9, 1992) we give a localization formula in equivariant cohomology in the case of a Hamiltonian torus action on a compact symplectic manifold X. The integral over X of an equivariant closed form can be written as an integral over the submanifold of critical points of the square of the moment map.