Quasi-hyperbolic planes in relatively hyperbolic groups

@article{Mackay2011QuasihyperbolicPI,
title={Quasi-hyperbolic planes in relatively hyperbolic groups},
author={J. M. Mackay and A. Sisto},
journal={arXiv: Group Theory},
year={2011}
}

We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the hyperbolic plane. In natural situations, the specific embeddings we find remain quasi-isometric embeddings when composed with the inclusion map from the Cayley graph to the coned-off graph, as well as when composed with the quotient map to "almost every" peripheral (Dehn) filling.
We apply our theorem to study the… Expand