Displacement techniques in bounded cohomology

Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commutator length. Recently, the authors introduced the property of commuting cyclic conjugates, a new displacement technique that is widely applicable and provides vanishing of the bounded cohomology in all positive degrees and all dual separable coefficients. In this note we consider the most recent along with the by now classical displacement techniques and we study implications among them as well as counterexamples.