Related papers: Two-dimensional Artin groups with CAT(0) dimension…

We show that the piecewise Euclidean Moussong metric on the Deligne complex of the Artin group of type $B_3$ is $\mathrm{CAT}(0)$. We do this by establishing a criteria for a complex made of $B_3$ simplices to be $\mathrm{CAT}(1)$ in terms…

We show that for $n \geq 3$, there are torsion-free CAT(0) groups with visual boundaries that embed into $S^n$ but which are not virtually the fundamental group of a compact aspherical $n+1$-manifold. The groups are the CAT(0) and not…

We define for every affine Coxeter graph a certain factor group of the associated Artin group and prove that some of these groups appear as orbifold fundamental groups of moduli spaces. Examples are the moduli space of nonsingular cubic…

We investigate the Tits boundary of locally compact CAT(0) 2-complexes. In particular we show that away from the endpoints, a geodesic segment in the Tits boundary is the ideal boundary of an isometrically embedded Euclidean sector. As…

We give concrete, "infinitesimal" conditions for a proper geodesically complete CAT(0) space to have semistable fundamental group at infinity.

We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

The irreducible euclidean Coxeter groups that naturally act geometrically on euclidean space are classified by the well-known extended Dynkin diagrams and these diagrams also encode the modified presentations that define the irreducible…

We exhibit a variety of groups that act properly and even cocompactly on median graphs (a.k.a. one-skeletons of CAT(0) cube complexes), with quasi-isometric groups that do not admit any proper action on a median graph. This answes a…

It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…

We provide a necessary and sufficient condition on a finite flag simplicial complex, L, for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to L. We then find new examples of such CAT(0) cube complexes…

In this paper, we study isometric actions on finite-dimensional CAT(0) spaces for the Higman-Thompson groups $T_n$, which are generalizations of Thompson's group $T$. It is known that every semi-simple action of $T$ on a complete CAT(0)…

We show that a certain triangulation of CAT(0) triangle-pentagon complexes is $7$-located and locally $5$-large. Hereby we give examples of $7$-located, locally $5$-large groups.

A common feature of Coxeter groups and right-angled Artin groups is their solution to the word problem. Matthew Dyer introduced a class of groups, which we call Dyer groups, sharing this feature. This class includes, but is not limited to,…

This is the second in a series of papers about torsion-free groups which act properly and cocompactly on a CAT(0) metric space with isolated flats and relatively thin triangles. Our approach is to adapt the methods of Sela and others for…

Even though big mapping class groups are not countably generated, certain big mapping class groups can be generated by a coarsely bounded set and have a well defined quasi-isometry type. We show that the big mapping class group of a stable…

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

Let $\pi$ be a group equipped with an action of a second group $G$ by automorphisms. We define the equivariant cohomological dimension ${\sf cd}_G(\pi)$, the equivariant geometric dimension ${\sf gd}_G(\pi)$, and the equivariant…

In this article, we state and prove a general criterion which prevents some groups from acting properly on finite-dimensional CAT(0) cube complexes. As an application, we show that, for every non-trivial finite group $F$, the lamplighter…

In this paper we consider the class of 2-dimensional Artin groups with connected, large type, triangle-free defining graphs (type CLTTF). We classify these groups up to isomorphism, and describe a generating set for the automorphism group…