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research article
Lamplighters and the bounded cohomology of Thompson's group
May 11, 2022
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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Name
s00039-022-00604-9.pdf
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Publisher's version
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openaccess
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CC BY
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294.22 KB
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Adobe PDF
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72c096af81627c370c6c9bca68d7955f