A note on arithmetic lattices in $\mathbb{H}^n$ and exotic subgroups of hyperbolic groups

Monika Kudlinska

Published 2023-03-20Version 1

We construct the first known infinite family of quasi-isometry classes of subgroups of hyperbolic groups which are not hyperbolic and are of type $\mathrm{FP}(\mathbb{Q})$. We give a simple criterion for producing many non-hyperbolic subgroups of hyperbolic groups with strong finiteness properties. We also observe that local hyperbolicity and algebraic fibring are mutually exclusive in higher dimensions.