On Cannon-Thurston maps for relatively hyperbolic groups
Group Theory
2012-06-27 v1 Geometric Topology
Abstract
Baker and Riley proved that a free group of rank 3 can be contained in a hyperbolic group as a subgroup for which the Cannon-Thurston map is not well-defined. By using their result, we show that the phenomenon occurs for not only a free group of rank 3 but also every non-elementary hyperbolic group. In fact it is shown that a similar phenomenon occurs for every non-elementary relatively hyperbolic group.
Keywords
Cite
@article{arxiv.1206.5868,
title = {On Cannon-Thurston maps for relatively hyperbolic groups},
author = {Yoshifumi Matsuda and Shin-ichi Oguni},
journal= {arXiv preprint arXiv:1206.5868},
year = {2012}
}
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7 pages