BOUNDED COHOMOLOGY AND BINATE GROUPS

Abstract A group is boundedly acyclic if its bounded cohomology with trivial real coefficients vanishes in all positive degrees. Amenable groups are acyclic, while the first nonamenable examples of compactly supported homeomorphisms $ {\mathbb {R}}^{n}$ (Matsumoto–Morita) and mitotic (Löh). We prove that binate (alias pseudo-mitotic) which provides a unifying approach to aforementioned results. Moreover, we show universally acyclic. obtain several new as well computations certain acting on circle. In particular, discuss how these results suggest Thompson F , T V simple possible.