English

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}
}

Comments

7 pages

R2 v1 2026-06-21T21:25:23.976Z