2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78904For an $S^{1}$-manifold with boundary, we prove a localization formula applying to any equivariant cohomology theory satisfying a certain algebraic condition. We show how the localization result of Kalkman and a case of the quantization commutes with reduction theorem follow easily from the localization formula.14 pagesDifferential GeometryAlgebraic TopologySymplectic Geometry57S15; 55N91; 19L47; 53C15text