9 problems

A diagram group is a group arising from a semigroup presentation and a base word. The Subgroup Conjecture. Every subgroup of a diagram group is itself a diagram group. The conjectu…

Let $G$ be a relatively hyperbolic diagram group. Free-product conjecture. Relatively hyperbolic diagram groups are free products. The claim gives a more precise form of the preced…

Let $G$ be a relatively hyperbolic diagram group, meaning that $G$ is relatively hyperbolic with respect to a specified collection of peripheral subgroups. Relative-hyperbolicity c…

Let $G$ be a diagram group, and let $\mathbb{Z} \wr \mathbb{Z}^2$ denote the wreath product of $\mathbb{Z}$ by $\mathbb{Z}^2$. Lamplighter exclusion conjecture. The group $G$ does…

Let $G$ be a diagram group, let $\mathbb{Z} \wr \mathbb{Z}$ denote the lamplighter group, and let a right-angled Artin group mean a group defined by a finite graph presentation wit…

Let $H$) be a subgroup of a diagram group $D(\mathcal{P},w)$, and let $\mathrm{Cl}(H)$ denote its closure obtained by folding the associated directed $2$-complex. The closure conta…

Let $\mathcal{K}$ be a directed $2$-complex, let $u$ be a $1$-path, and let $H$ be a subgroup of the diagram group $\mathrm{DG}(\mathcal{K},u)$. A subgroup is closed for components…

Let $D(\mathcal{P},w)$ be a diagram group, and let $A(\mathcal{P},w)$ denote the associated right-angled Artin group. A diagram group is embeddable into a right-angled Artin group…

Let $P$ be a semigroup presentation, let $w$ be a word in the semigroup presented by $P$, and let $D(P,w)$ be the associated diagram group acting on the proper CAT(0) cube complex…