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Groups, Geometry, and Dynamics


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Volume 4, Issue 3, 2010, pp. 533–548
DOI: 10.4171/GGD/94

Published online: 2010-06-16

Codimension one subgroups and boundaries of hyperbolic groups

Thomas Delzant[1] 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