We construct an embedding of any right-angled Artin group into a graph braid group. We include an observation which decreases the number of strands of the graph braid group required for this embedding, yielding an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.

This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a 2-dimensional Artin group the Deligne complex is Gromov hyperbolic preci...

We prove that any standard parabolic subgroup of any Artin group is convex with respect to the standard generating set.

In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph Γ, we produce a new graph through a purely combinatorial procedure, and call it the extension graph Γ of Γ. We produce a second graph Γ k , the clique graph of Γ, by adding extra vertices for each complete subgraph of Γ. We prove that each finite induced subgraph Λ of Γ gives ris...

The goal of this mostly expository paper is to present several candidates for hyperbolic structures on irreducible Artin-Tits groups spherical type and elucidate some relations between them. Most constructions are algebraic analogues previously known Artin braid coming from natural actions these curve graphs (modified) arc punctured disks.