Virtual splittings of right-angled Artin groups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912990071095296 |
|---|---|
| author | Bensaid, Oussama Genevois, Anthony Tessera, Romain |
| author_facet | Bensaid, Oussama Genevois, Anthony Tessera, Romain |
| contents | In this article, we determine, given a finite graph $Γ$ and an integer $n \geq 1$, when a right-angled Artin group $A(Γ)$ virtually splits over an abelian subgroup of rank $n$. More precisely, we show that the following assertions are equivalent: (1) $A(Γ)$ admits $\mathbb{Z}^n$ as a codimension-one subgroup, (2) $A(Γ)$ virtually splits over $\mathbb{Z}^n$, (3) $A(Γ)$ splits over $\mathbb{Z}^n$, and (4) $Γ$ either is a complete graph with $n+1$ vertices or contains a complete subgraph of size $n$ that has a subgraph separating $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29008 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Virtual splittings of right-angled Artin groups Bensaid, Oussama Genevois, Anthony Tessera, Romain Group Theory 20F65, 20F69 In this article, we determine, given a finite graph $Γ$ and an integer $n \geq 1$, when a right-angled Artin group $A(Γ)$ virtually splits over an abelian subgroup of rank $n$. More precisely, we show that the following assertions are equivalent: (1) $A(Γ)$ admits $\mathbb{Z}^n$ as a codimension-one subgroup, (2) $A(Γ)$ virtually splits over $\mathbb{Z}^n$, (3) $A(Γ)$ splits over $\mathbb{Z}^n$, and (4) $Γ$ either is a complete graph with $n+1$ vertices or contains a complete subgraph of size $n$ that has a subgraph separating $Γ$. |
| title | Virtual splittings of right-angled Artin groups |
| topic | Group Theory 20F65, 20F69 |
| url | https://arxiv.org/abs/2603.29008 |