Lamplighters and the bounded cohomology of Thompson’s group

Abstract We prove the vanishing of bounded cohomology lamplighter groups for a wide range coefficients. This implies same number with self-similarity properties, such as Thompson’s group F . In particular, these are boundedly acyclic. Our method is ergodic and applies to “large” transformation where Mather–Matsumoto–Morita sometimes fails because not all acyclic in usual sense.