Codimension one subgroups and boundaries of hyperbolic groups

Details Codimension one subgroups and boundaries of hyperbolic groups Codimension one subgroups and boundaries of hyperbolic groups

2008-07-18

arxiv.org/abs/0807.2932v1

Mathematics

Group Theory

Scientific paper

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 can not be
extended to splittings over more complicated subgroups.

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