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arXiv · 2010.03421

Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut

Nima Hoda·Suraj Krishna M S
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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.

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Nima Hoda, Suraj Krishna M S. 2020-10-07. Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut. https://doi.org/10.1017/s0305004123000208

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