Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut
arXiv:2010.03421 · doi:10.1017/S0305004123000208
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.
14 pages, 6 figures