We obtain a characterisation of confined subgroups of Thompson's group $F$. As a result, we deduce that the orbital graph of a point under an action of $F$ has uniformly subexponential growth if and only if this point is fixed by the commutator subgroup. This allows us to prove non-embeddability of $F$ into wobbling groups of graphs with uniformly subexponential growth.

中文翻译：

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汤普森群 $F$ 的受限子群及其嵌入摆动群

我们获得了 Thompson 群 $F$ 的受限子群的特征。因此，我们推论，当且仅当该点由交换子子群固定时，在 $F$ 作用下的点的轨道图具有均匀的次指数增长。这使我们能够证明 $F$ 不可嵌入到具有均匀次指数增长的摆动图组中。