  Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on the manifold
$M$ by diffeomorphisms one can define the $\Gamma$-co-invariant cohomology of
$M$ to be the cohomology of the differential complex
$\Omega_c(M)_\Gamma=\mathrm{span}\{\omega-\gamma^*\omega,\;\omega\in\Omega_c(M),\;\gamma\in\Gamma\}.$
For a Lie algebra $\mathcal{G}$ acting on the manifold $M$, one defines the
cohomology of $\mathcal{G}$-divergence forms to be the cohomology of the
complex
$\mathcal{C}_{\mathcal{G}}(M)=\mathrm{span}\{L_X\omega,\;\omega\in\Omega_c(M),\;X\in\mathcal{G}\}.$
In this short paper we present a situation where these two cohomologies are
infinite dimensional.
