2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169016We describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern-Weil homomorphism to the twisted equivariant cohomology. We clarify that in order to have a cohomology theory, the coefficients of the twisted equivariant cohomology must be taken in the completed polynomial algebra over the dual Lie algebra of $G$. We recall the relation between the equivariant cohomology of exact Courant algebroids and the twisted equivariant cohomology, and we show how to endow with a generalized complex structure the finite dimensional approximations of the Borel construction $M\times_G EG_k$, whenever the generalized complex manifold $M$ possesses a Hamiltonian $G$ action.21 pagesDifferential GeometryAlgebraic Topology55N91, 37K65text