Related papers: Acylindrical hyperbolicity for Artin groups with a…

We give criteria for a graph of groups to have finite stature with respect to its collection of vertex groups, in the sense of Huang-Wise. We apply it to the triangle Artin groups that were previously shown to split as a graph of groups.…

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin-Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the…

We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, $G$ admits quasi-isometric group embeddings into a pure…

A group G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that every acylindrically hyperbolic group G has a generating set X such that the corresponding Cayley graph is a…

We introduce and investigate the ribbon groupoid associated with a Garside group. Under a technical hypothesis, we prove that this category is a Garside groupoid. We decompose this groupoid into a semi-direct product of two of its parabolic…

We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is…

En nous basant sur les r\'esultats d'Arthur annonc\'es dans \cite[\S 30]{Arthur} nous d\'emontrons les conjectures \'enonc\'ees dans \cite{IMRN,BC,SMF} dans le cas des groupes orthogonaux \`a l'exclusion des groupes de type ${}^6 - D_4$. En…

We study coarse separation in one-ended hyperbolic groups from a quantitative point of view, focusing on the volume growth of separating subsets. We prove that a one-ended hyperbolic group that is not virtually a surface group is coarsely…

We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\Z$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers of an infinite order…

We show that for a large class of Artin groups with Dynkin diagrams being a tree, the $K(\pi,1)$-conjecture holds. We also establish the $K(\pi,1)$-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which…

Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a non-compact hyperbolic $3$-manifold such as a hyperbolic knot complement. We prove a rigidity result saying that if two non-elementary relatively…

We prove that triangle Artin groups of the type $A_{2,3,2n}$ are residually finite for all $n\geq4$. This requires splitting these triangle Artin groups as graphs of groups and then proving that each of these graphs of groups has finite…

We give a criterion to prove that some groups are not acylindrically hyperbolic. As an application, we prove that the mapping class group of an infinite type surface is not acylindrically hyperbolic.

We show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative: their subgroups either contain a non-abelian free group or are virtually free abelian of rank at most $2$. When in addition the associated Coxeter…

We give a necessary and sufficient condition for a 2-dimensional or a three-generator Artin group $A$ to be (virtually) cocompactly cubulated, in terms of the defining graph of $A$.

A number of properties of spherical Artin groups extend to Garside groups, defined as the groups of fractions of monoids where least common multiples exist, there is no nontrivial unit, and some additional finiteness conditions are…

We prove that a parabolic subgroup $P$ contained in another parabolic subgroup $P'$ of an Artin group $A$ is a parabolic subgroup of $P'$. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our…

We introduce the notion of finite stature of a family $\{H_i\}$ of subgroups of a group $G$. We investigate the separability of subgroups of a group $G$ that splits as a graph of hyperbolic special groups with quasiconvex edge groups. We…

In this paper we solve the isomorphism problem for all large-type Artin groups. Our strategy involves reconstructing the Coxeter groups associated with large-type Artin groups in a purely algebraic way. This answers several questions raised…

We prove that most Artin groups of large and hyperbolic type are Hopfian, meaning that every self-epimorphism is an isomorphism. The class covered by our result is generic, in the sense of Goldsborough-Vaskou. Moreover, assuming the…