Let $X$ a manifold and $G$ a group that acts on X freely, properly, and smoothly. The quotient $X/G$ has a manifold structure such the projection $\pi:X\rightarrow X/G$ is a submersion. My question is: how are related the De Rham´s cohomology groups of $X$ with the De Rham´s cohomology groups of the quotient?
Thank you for your time.