Groups, Geometry, and Dynamics
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Published online: 2010-06-16
Codimension one subgroups and boundaries of hyperbolic groupsThomas Delzant and Panos Papasoglu (1) Université de Strasbourg, France
We 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 cannot be extended to splittings over more complicated subgroups.
Keywords: Boundary, hyperbolic group, splittings
Delzant Thomas, Papasoglu Panos: Codimension one subgroups and boundaries of hyperbolic groups. Groups Geom. Dyn. 4 (2010), 533-548. doi: 10.4171/GGD/94