Relative hyperbolicity of hyperbolic-by-cyclic groups - Archive ouverte HAL
Article Dans Une Revue Groups, Geometry, and Dynamics Année : 2023

Relative hyperbolicity of hyperbolic-by-cyclic groups

Résumé

Let G be a torsion-free hyperbolic group and α an automorphism of G. We show that there exists a canonical collection of subgroups that are polynomially growing under α, and that the mapping torus of G by α is hyperbolic relative to the suspensions of the maximal polynomially growing subgroups under α. As a consequence, we obtain a dichotomy for growth: given an automorphism of a torsion-free hyperbolic group, the conjugacy class of an element either grows polynomially under the automorphism, or at least exponentially.
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hal-03949598 , version 1 (17-09-2024)

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François Dahmani, Suraj Krishna M S. Relative hyperbolicity of hyperbolic-by-cyclic groups. Groups, Geometry, and Dynamics, 2023, 17 (2), pp.403-426. ⟨10.4171/ggd/703⟩. ⟨hal-03949598⟩
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