On the equivariant de Rham cohomology for non-compact Lie groups

Let G be a connected and non-necessarily compact Lie group acting on a connected manifold M. In this short note we announce the following result: for a G-invariant closed differential form on M, the existence of a closed equivariant extension in the Cartan model for equivariant cohomology is equivalent to the existence of an extension in the homotopy quotient.