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We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings’ foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be -dimensional. More specifically, given a non-quasiconvex subgroup of a (possibly non-hyperbolic) RACG, our construction gives a corresponding non-quasiconvex subgroup of a hyperbolic RACG. We use this to construct explicit examples of non-quasiconvex subgroups of hyperbolic RACGs including subgroups whose generators are as short as possible (length two words), finitely generated free subgroups, non-finitely presentable subgroups, and subgroups of fundamental groups of square complexes of nonpositive sectional curvature.
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Special IMM Groups
Italiano–Martelli–Migliorini recently constructed hyperbolic groups which have non-hyperbolic subgroups of finite type. Using a closely related construction, Llosa Isenrich–Martelli–Py constructed hyperbolic groups with subgroups of type F3 but not F4. We observe that these hyperbolic groups can be chosen to be special in the sense of Haglund–Wise.
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- Award ID(s):
- 1904913
- PAR ID:
- 10475806
- Publisher / Repository:
- London Mathematical Society
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 54
- Issue:
- 2
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- 428 to 448
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1112/blms.12571
