2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72186In our book on cohomological methods in transformation groups the minimal Hirsch-Brown model was used to good effect. The construction there, however, was rather abstract. Here, for smooth compact connected Lie group actions on smooth closed manifolds, we give a much more explicit construction of the minmal Hirsch-Brown model using operators from classical Hodge theory and the small Cartan model. As a simple example, we discuss circle actions on complex projective space, computing the deformation terms in the product by means of the moment map in two different ways.14 pagesDifferential GeometrySymplectic Geometry57S15 (Primary) 53D20 (Secondary)text