JournalsggdVol. 4, No. 3pp. 533–548

Codimension one subgroups and boundaries of hyperbolic groups

  • Thomas Delzant

    Université de Strasbourg, France
  • Panos Papasoglu

    University of Athens, Greece
Codimension one subgroups and boundaries of  hyperbolic groups cover
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Abstract

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.

Cite this article

Thomas Delzant, Panos Papasoglu, Codimension one subgroups and boundaries of hyperbolic groups. Groups Geom. Dyn. 4 (2010), no. 3, pp. 533–548

DOI 10.4171/GGD/94