2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165239We construct hyperbolic groups with the following properties: The boundary of the group has big dimension, it is separated by a Cantor set and the group does not split. This shows that Bowditch's theorem that characterizes splittings of hyperbolic groups over 2-ended groups in terms of the boundary can not be extended to splittings over more complicated subgroups.Group Theorytext