Codimension one subgroups and boundaries of hyperbolic groups

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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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Group Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/165239

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.2932
 http://arxiv.org/abs/0807.2932

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arXiv