Confined subgroups of Thompson's group \(F\) and its embeddings into wobbling groups (Q2245016)

Summary: 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.