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arXiv · 2610.27932

Thompson's group $F$ is not weakly amenable

Koji Fujiwara
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Abstract

Let $F$ be Thompson's group, and let $D$ be the set of dyadic rationals in $[0,1]$. We give an embedding of $\mathbb Z^{(D)}\rtimes F$ into $F$, where the semidirect product is defined by the natural action of $F$ on $D$. Using this embedding, we deduce from the nonamenability of $F$ that $F$ is not weakly amenable.

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Koji Fujiwara. 2026-10-20. Thompson's group $F$ is not weakly amenable. https://arxiv.org/abs/2610.27932

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