An infinite family of exotic subgroups of hyperbolic groups

Abstract

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.

arXiv commentNew background section. All results remain unchanged. This is the version accepted for publication in the Proceedings of the American Mathematical Society