A note on bounded-cohomological dimension of discrete groups
arXiv:1504.05760
Abstract
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.
18 pages, 1 figure; v2: corrected typos, reorganisation, to appear in JMSJ