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arXiv · 1206.5868

On Cannon-Thurston maps for relatively hyperbolic groups

Yoshifumi Matsuda·Shin-ichi Oguni
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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.

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Yoshifumi Matsuda, Shin-ichi Oguni. 2012-06-26. On Cannon-Thurston maps for relatively hyperbolic groups. https://arxiv.org/abs/1206.5868

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