Relative hyperbolicity of hyperbolic-by-cyclic groups

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 $\alpha$.

21 pages, 1 figure. v2: Incorporates referee comments

References in corpus (1)

• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth

Cited by in corpus (2)

• Cubulating a free-product-by-cyclic group
• Reducing the conjugacy problem for relatively hyperbolic automorphisms to peripheral components