Lamplighters and the bounded cohomology of Thompson's group
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Publication:6386797
DOI10.1007/S00039-022-00604-9arXiv2112.13741MaRDI QIDQ6386797
Publication date: 27 December 2021
Abstract: We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range of coefficients. This implies the same vanishing for a number of groups with self-similarity properties, such as Thompson's group F. In particular, these groups are boundedly acyclic. Our method is ergodic and applies to large transformation groups where the Mather-Matsumoto-Morita method sometimes fails because not all are acyclic in the usual sense.
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