Bounded cohomology of transformation groups in all degrees

Let $M$ be a compact connected oriented smooth manifold, of dimension $n\ge2$. Let $\mathcal T_MG$ be one of the following transformation groups: $Homeo_0(M,μ)$, $Diff_0(M,μ)$, $Symp_0(M, ω)$ (in case $M$ is symplectic) and $Ham(M, ω)$ (in case $M$ is symplectic). Denote by $\overline{H}_b^d(\mathca