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.
1
Université de Strasbourg, France
2
University of Athens, Greece
Thomas Delzant; Panos Papasoglu. Codimension one subgroups and boundaries of hyperbolic groups. Groups, geometry, and dynamics, Tome 4 (2010) no. 3, pp. 533-548. doi: 10.4171/ggd/94
@article{10_4171_ggd_94,
author = {Thomas Delzant and Panos Papasoglu},
title = {Codimension one subgroups and boundaries of hyperbolic groups},
journal = {Groups, geometry, and dynamics},
pages = {533--548},
year = {2010},
volume = {4},
number = {3},
doi = {10.4171/ggd/94},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/94/}
}
TY - JOUR
AU - Thomas Delzant
AU - Panos Papasoglu
TI - Codimension one subgroups and boundaries of hyperbolic groups
JO - Groups, geometry, and dynamics
PY - 2010
SP - 533
EP - 548
VL - 4
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/94/
DO - 10.4171/ggd/94
ID - 10_4171_ggd_94
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