Publication

Lamplighters and the bounded cohomology of Thompson's group

Nicolas Monod
2022
Journal Articles

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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Lamplighters and the bounded cohomology of Thompson's group

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