Related papers: Right-angled Coxeter quandles and polyhedral produ…

We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group $W$ and relate it to the descent algebra of $W$. As a result, we claim that both the group algebra of $W$, as well as the…

We introduce and study the operation, called dense amalgam, which to any tuple X_1,...,X_k of non-empty compact metric spaces associates some disconnected perfect compact metric space, denoted $\widetilde\sqcup(X_1,...,X_k)$, in which there…

We define the Chow ring of the classifying space of a linear algebraic group. In all the examples where we can compute it, such as the symmetric groups and the orthogonal groups, it is isomorphic to a natural quotient of the complex…

We study the algebraic rank of various classes of $\mathrm{CAT}(0)$ groups. They include right-angled Coxeter groups, right-angled Artin groups, relatively hyperbolic groups and groups acting geometrically on $\mathrm{CAT}(0)$ spaces with…

We retrieve the graded commutative algebra structure of rack and quandle cohomology by purely algebraic means.

We prove that an object $U$ in a triangulated category with coproducts is silting if and only if it is a (weak) generator of the category, the orthogonal class $U^{\perp_{>0}}$ contains $U$, and $U^{\perp_{>0}}$ is closed under direct sums.…

For any finite Coxeter group W, we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W. The…

Here, for $W$ the Coxeter group $\mathrm{D}_n$ where $n > 4$, it is proved that the maximal rank of an abstract regular polytope for $W$ is $n - 1$ if $n$ is even and $n$ if $n$ is odd. Further it is shown that $W$ has abstract regular…

The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that…

Let $W$ be an irreducible Coxeter group. We define the Coxeter pop-stack-sorting operator $\mathsf{Pop}:W\to W$ to be the map that fixes the identity element and sends each nonidentity element $w$ to the meet of the elements covered by $w$…

We compute the group homology, the algebraic $K$- and $L$-groups, and the topological $K$-groups of right-angled Artin groups, right-angled Coxeter groups, and more generally, graph products.

The descent algebra of a finite Coxeter group $W$ is a basic algebra, and as such it has a presentation as quiver with relations. In recent work, we have developed a combinatorial framework which allows us to systematically compute such a…

We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let $\Gamma_1,\Gamma_2$ be joins of finite generalized thick $m$-gons with $m\geq 3$. We show that the corresponding right-angled Coxeter groups are…

Given two correspondences $X$ and $Y$ and a discrete group $G$ which acts on $X$ and coacts on $Y$, one can define a twisted tensor product $X\boxtimes Y$ which simultaneously generalizes ordinary tensor products and crossed products by…

We show that for a large class $\mathcal{W}$ of Coxeter groups the following holds: Given a group $W_\Gamma$ in $\mathcal{W}$, the automorphism group ${\rm Aut}(W_\Gamma)$ virtually surjects onto some infinite Coxeter group. In particular,…

A panel structure on a topological space is just a locally finite family of closed subspaces. A space together with a panel structure is called a space with faces. In this paper, we introduce a notion of polyhedral product over a space with…

We study the model theory of countable right-angled buildings with infinite residues. For every Coxeter graph we obtain a complete theory with a natural axiomatisation, which is $\omega$-stable and equational. Furthermore, we provide sharp…

In this article, we introduce and investigate a class of C$^{\ast}$-algebras generated by reduced graph products of C$^{\ast}$-algebras, augmented with families of projections naturally associated with words in right-angled Coxeter groups.…

We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential or infinite. We prove that a RACG is strongly…

The deletion order of a finitely generated Coxeter group W is a total order on the elements which, as is proved, is a refinement of the Bruhat order. This order is applied in [8] to construct Elnitsky tilings for any finite Coxeter group.…