We inspect the normal subgroup structure of the braided Thompson groups and . We prove that every proper normal subgroup of lies in the kernel of the natural quotient , and we exhibit some families of interesting such normal subgroups. For , we prove that for any normal subgroup of , either is contained in the kernel of , or else contains . We also compute the Bieri–Neumann–Strebel invariant , which is a useful tool for understanding normal subgroups containing the commutator subgroup.
Cite this article
Matthew C.B. Zaremsky, On normal subgroups of the braided Thompson groups. Groups Geom. Dyn. 12 (2018), no. 1, pp. 65–92DOI 10.4171/GGD/438