The Kernel of the Equivariant Kirwan Map and the Residue Formula

Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced directly from the residue theorem of Jeffrey and Kirwan. A characterization of the kernel of the Kirwan map in terms of residues of one variable (i.e. associated to Hamiltonian circle actions) is obtained.