Subgroups of word hyperbolic groups in rational dimension 2 (Q2035108)

Summary: 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.