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Relative hyperbolicity of hyperbolic-by-cyclic groups (2006.07288v2)
Published 12 Jun 2020 in math.GR
Abstract: Let $G$ be a torsion-free hyperbolic group and $\alpha$ an automorphism of $G$. We show that there exists a canonical collection of subgroups that are polynomially growing under $\alpha$, and that the mapping torus of $G$ by $\alpha$ is hyperbolic relative to the suspensions of the maximal polynomially growing subgroups under $\alpha$.