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arXiv · 2112.13741

Lamplighters and the bounded cohomology of Thompson's group

Nicolas Monod
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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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Nicolas Monod. 2021-12-27. Lamplighters and the bounded cohomology of Thompson's group. https://arxiv.org/abs/2112.13741

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