We obtain a characterisation of confined subgroups of Thompson's group . As a result, we deduce that the orbital graph of a point under an action of has uniformly subexponential growth if and only if this point is fixed by the commutator subgroup. This allows us to prove non-embeddability of into wobbling groups of graphs with uniformly subexponential growth.
Cite this article
Maksym Chaudkhari, Confined subgroups of Thompson's group and its embeddings into wobbling groups. Groups Geom. Dyn. 15 (2021), no. 2, pp. 491–501DOI 10.4171/GGD/604