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

Abstract

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.

arXiv comment5 pages. Minor corrections. To appear in DGA