The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Groups, Geometry, and Dynamics


Full-Text PDF (199 KB) | Metadata | Table of Contents | GGD summary
Online access to the full text of Groups, Geometry, and Dynamics is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 15, Issue 1, 2021, pp. 83–100
DOI: 10.4171/GGD/592

Published online: 2020-12-29

Subgroups of word hyperbolic groups in rational dimension 2

Shivam Arora[1] and Eduardo Martínez-Pedroza[2]

(1) Memorial University of Newfoundland, St John's, Canada
(2) Memorial University of Newfoundland, St John's, Canada

A result of Gersten states that if $G$ is a hyperbolic group with integral cohomological dimension $\mathsf{cd}_{\mathbb{Z}}(G)=2$ then every finitely presented subgroup is hyperbolic. We generalize this result for the rational case $\mathsf{cd}_{\mathbb{Q}}(G)=2$. In particular, the result applies to the class of torsion-free hyperbolic groups $G$ with $\mathsf{cd}_{\mathbb Z}(G)=3$ and $\mathsf{cd}_{\mathbb Q}(G)=2$ discovered by Bestvina and Mess.

Keywords: Hyperbolic group, cohomological dimension, finiteness properties, homological Dehn function

Arora Shivam, Martínez-Pedroza Eduardo: Subgroups of word hyperbolic groups in rational dimension 2. Groups Geom. Dyn. 15 (2021), 83-100. doi: 10.4171/GGD/592