The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
| dc.creator | Gautero, Francois | |
| dc.creator | Lustig, Martin | |
| dc.date | 2007-07-05 | |
| dc.date | 2008-10-26 | |
| dc.date.accessioned | 2026-07-07T10:12:48Z | |
| dc.date.available | 2026-07-07T10:12:48Z | |
| dc.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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/0707.0822 | |
| dc.identifier | http://arxiv.org/abs/0707.0822 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172305 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F65 | |
| dc.title | The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth | |
| dc.type | text |