Oli Jones

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20232026

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math.GR2026

A virtual RAAG with no finite index normal RAAG

Oli Jones

In this note, we exhibit a group which has a right-angled Artin group as a finite index subgroup, but no finite index normal subgroup isomorphic to any right-angled Artin group. Th…

math.GR2025

Fixed subgroups of generalised Baumslag-Solitar groups

Oli Jones, Alan Logan

We investigate fixed subgroups of automorphisms of generalised Baumslag-Solitar (GBS) groups. Our main results are for automorphisms leaving a Bass-Serre tree invariant, under the…

math.GR2024

Type VF for outer automorphism groups of large-type Artin groups

Oli Jones

Given a connected large-type Artin group $A_{Γ}$ , we introduce a deformation space $D$ . If $Γ$ is triangle-free, or has all labels at least 6, we show that this space is ca…

math.GR2024

Fixed subgroups in Artin groups

Oli Jones, Nicolas Vaskou

We study fixed subgroups of automorphisms of any large-type Artin group $A_{Γ}$ . We define a natural subgroup $Aut_{Γ} (A_{Γ})$ of $Aut (A_{Γ})$ , and for every $γ\in \mathr…

math.GR2023

Fixed Points of Automorphisms of Torus Knot Groups

Oli Jones

We completely classify fixed point subgroups in Torus Knot Groups, that is groups of the form $G_{p, q} = ⟨ x, y ∣ x^{p} = y^{q} ⟩$ . We not only give the isomorphism type,…