Document Type
Article
Publication Date
2-1-2023
Abstract
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 2-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.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
First Page
1427
Last Page
1444
Recommended Citation
Dani, P., & Levcovitz, I. (2023). NON-QUASICONVEX SUBGROUPS OF HYPERBOLIC GROUPS VIA STALLINGS-LIKE TECHNIQUES. Transactions of the American Mathematical Society, 376 (2), 1427-1444. https://doi.org/10.1090/tran/8801