2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61869We show that for a Hamiltonian action of a compact torus $G$ on a compact, connected symplectic manifold $M$, the $G$-equivariant cohomology is determined by the residual $S^1$ action on the submanifolds of $M$ fixed by codimension-1 tori. This theorem allows us to compute the equivariant cohomology of certain manifolds, which have pieces that are four-dimensional or smaller. We give several examples of the computations that this allows.13 pages, 4 figuresSymplectic Geometry53D05 (primary); 53D20,55N91 (secondary)text