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 non-amenable examples were the group of compactly supported homeomorphisms of Rn (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.

Francesco Fournier-Facio, Clara Löh, Marco Moraschini (2023). Bounded cohomology and binate groups. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 115(2), 204-239 [10.1017/S1446788722000106].

Bounded cohomology and binate groups

Marco Moraschini
2023

Abstract

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 non-amenable examples were the group of compactly supported homeomorphisms of Rn (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.
2023
Francesco Fournier-Facio, Clara Löh, Marco Moraschini (2023). Bounded cohomology and binate groups. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 115(2), 204-239 [10.1017/S1446788722000106].
Francesco Fournier-Facio; Clara Löh; Marco Moraschini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/880055
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