PolExp growth for automorphisms of toral relatively hyperbolic groups
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912751256862720 |
|---|---|
| author | Coulon, Rémi Hilion, Arnaud Horbez, Camille Levitt, Gilbert |
| author_facet | Coulon, Rémi Hilion, Arnaud Horbez, Camille Levitt, Gilbert |
| contents | Let $G$ be a toral relatively hyperbolic group, and let $φ\in\mathrm{Aut}(G)$. We prove that, under iteration of $φ$, the conjugacy length $||φ^n(g)||$ of every element $g\in G$ grows like $n^dλ^n$ for some $d\in\mathbb{N}$ and some algebraic integer $λ\geq 1$. For a given $φ$, only finitely many values of $d$ and $λ$ occur as $g$ varies in $G$. The same statements hold for the growth of the word length $|φ^n(g)|$.
For $G$ hyperbolic, we generalize polynomial subgroups: we show that, for a given growth type $n^dλ^n$ other than $1$, there is a malnormal family of quasiconvex subgroups $K_1,\dots,K_p$ such that a conjugacy class $[g]$ grows at most like $n^dλ^n$ if and only if $g$ is conjugate into one of the subgroups $K_i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PolExp growth for automorphisms of toral relatively hyperbolic groups Coulon, Rémi Hilion, Arnaud Horbez, Camille Levitt, Gilbert Group Theory Let $G$ be a toral relatively hyperbolic group, and let $φ\in\mathrm{Aut}(G)$. We prove that, under iteration of $φ$, the conjugacy length $||φ^n(g)||$ of every element $g\in G$ grows like $n^dλ^n$ for some $d\in\mathbb{N}$ and some algebraic integer $λ\geq 1$. For a given $φ$, only finitely many values of $d$ and $λ$ occur as $g$ varies in $G$. The same statements hold for the growth of the word length $|φ^n(g)|$. For $G$ hyperbolic, we generalize polynomial subgroups: we show that, for a given growth type $n^dλ^n$ other than $1$, there is a malnormal family of quasiconvex subgroups $K_1,\dots,K_p$ such that a conjugacy class $[g]$ grows at most like $n^dλ^n$ if and only if $g$ is conjugate into one of the subgroups $K_i$. |
| title | PolExp growth for automorphisms of toral relatively hyperbolic groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2512.05569 |