2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60866This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action.17 pages. Version 2 corrects typos in Th. 2, proof of Prop. 13, and the description of sections of Ad PDifferential GeometryAlgebraic Topology57R20; 55R40; 55N25text