JournalsggdVol. 15, No. 1pp. 83–100

Subgroups of word hyperbolic groups in rational dimension 2

  • Shivam Arora

    Memorial University of Newfoundland, St John's, Canada
  • Eduardo Martínez-Pedroza

    Memorial University of Newfoundland, St John's, Canada
Subgroups of word hyperbolic groups in rational dimension 2 cover
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Abstract

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

Cite this article

Shivam Arora, Eduardo Martínez-Pedroza, Subgroups of word hyperbolic groups in rational dimension 2. Groups Geom. Dyn. 15 (2021), no. 1, pp. 83–100

DOI 10.4171/GGD/592