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

如果一个群与平凡实数系数的有界上同调在所有正度都消失，则该群是有界无环的。顺应群是有界无环的，而第一个不可命名的例子是$ {\mathbb {R}}^{n}$ (Matsumoto-Morita) 和有丝分裂群 (Löh)的紧支持同胚群。我们证明二元（又名伪有丝分裂）群是有界无环的，这为上述结果提供了统一的方法。此外，我们证明二元群普遍有界无环。我们获得了有界无环群的几个新例子以及作用于圆的某些群的有界上同调的计算。特别是，我们讨论这些结果如何表明 Thompson 群F的有界上同调，T和V尽可能简单。