Let $G$ be a connected Lie group. We show that all characteristic classes of $G$ are bounded—when viewed in the cohomology of the classifying space of the group $G$ with the discrete topology—if and only if the derived group of the radical of $G$ is simply connected in its Lie group topology. We also give equivalent conditions in terms of stable commutator length and distortion.
"Bounded characteristic classes and flat bundles." J. Differential Geom. 95 (1) 39 - 51, September 2013. https://doi.org/10.4310/jdg/1375124608