Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to groups with infinite bounded-cohomological dimension, and we will provide new examples of groups with bounded-cohomological dimension equal to 0. In particular, we will prove that every group functorially embeds into an acyclic group with trivial bounded cohomology.
"A note on bounded-cohomological dimension of discrete groups." J. Math. Soc. Japan 69 (2) 715 - 734, April, 2017. https://doi.org/10.2969/jmsj/06920715