Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut
Group Theory
2023-10-24 v3
Abstract
We show that a group that is hyperbolic relative to strongly shortcut groups is itself strongly shortcut, thus obtaining new examples of strongly shortcut groups. The proof relies on a result of independent interest: we show that every relatively hyperbolic group acts properly and cocompactly on a graph in which the parabolic subgroups act properly and cocompactly on convex subgraphs.
Cite
@article{arxiv.2010.03421,
title = {Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut},
author = {Nima Hoda and Suraj Krishna M S},
journal= {arXiv preprint arXiv:2010.03421},
year = {2023}
}
Comments
14 pages, 6 figures