An infinite family of exotic subgroups of hyperbolic groups

Monika Kudlinska

An infinite family of exotic subgroups of hyperbolic groups

Group Theory 2024-04-18 v3

Authors: Monika Kudlinska

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.

Keywords

hyperbolic groups subgroups quasi-isometry fp property algebraic fibring local hyperbolicity

Cite

@article{arxiv.2303.11218,
  title  = {An infinite family of exotic subgroups of hyperbolic groups},
  author = {Monika Kudlinska},
  journal= {arXiv preprint arXiv:2303.11218},
  year   = {2024}
}

Comments

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

An infinite family of exotic subgroups of hyperbolic groups

Abstract

Keywords

Cite

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