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On Cannon-Thurston maps for relatively hyperbolic groups (1206.5868v1)
Published 26 Jun 2012 in math.GR and math.GT
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.