The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We prove that the mapping torus group $\FN \rtimes_α \Z$ of any automorphism $α$ of a free group $\FN$ of finite rank $n \geq 2$ is weakly hyperbolic relative to the canonical (up to conjugation) family $\mathcal H(α)$ of subgroups of $\FN$ which consists of (and contains representatives of all) conjugacy classes that grow polynomially under iteration of $α$. Furthermore, we show that $\FN \rtimes_α \Z$ is strongly hyperbolic relative to the mapping torus of the family $\mathcal H(α)$. As an application, we use a result of Drutu-Sapir to deduce that $\FN \rtimes_α \Z$ has Rapic Decay.
40 pages, no figure. Differences with respect to the first version: there is now an Appendix about $β$-train tracks, written by the second author. A Corollary about Rapid Decay for free-by-cyclic groups has been added
40 pages, no figure. Differences with respect to the first version: there is now an Appendix about $β$-train tracks, written by the second author. A Corollary about Rapid Decay for free-by-cyclic groups has been added