Related papers: Right-angled Artin groups, polyhedral products and…

The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type…

Given an associative algebra H, a linear space U and some linear maps J, T, \gamma , \eta satisfying some axioms, we define an associative algebra structure on U\otimes H, called an L-R-crossed product. This contains as particular cases…

Let [X/G] be a smooth Deligne-Mumford quotient stack. In a previous paper the authors constructed a class of exotic products called inertial products on K(I[X/G]), the Grothendieck group of vector bundles on the inertia stack I[X/G]. In…

Let $G$ be 2-generated group. The generating graph $\Gamma(G)$ of $G$ is the graph whose vertices are the elements of $G$ and where two vertices $g$ and $h$ are adjacent if $G = \langle g, h \rangle.$ This definition can be extended to a…

Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant…

The unordered configuration space of $n$ points on a graph $\Gamma,$ denoted here by $UC^n(\Gamma),$ can be viewed as the space of all configurations of $n$ unlabeled robots on a system of one-dimensional tracks, which is interpreted as a…

We show that the topological complexity of an aspherical space $X$ is bounded below by the cohomological dimension of the direct product $A\times B$, whenever $A$ and $B$ are subgroups of $\pi_1(X)$ whose conjugates intersect trivially. For…

Let $G$ be the multiplicative group generated by the gamma functions $\Gamma(ax+1)$ $(a=1,2,\dots)$, and $H$ be the subgroup of all elements of $G$ that converge to nonzero constants as $x\rightarrow\infty$. The quotient group $G/H$ is the…

We determine the epimorphisms $A \to W$ from the Artin group $A$ of type $\Gamma$ onto the Coxeter group $W$ of type $\Gamma$, in case $\Gamma$ is an irreducible Coxeter graph of spherical type, and we prove that the kernel of the standard…

The main goal of this paper is a calculation of the integral (co)homology of the group of symmetric automorphisms of a free product. We proceed by giving a geometric interpretation of symmetric automorphisms via a moduli space of certain…

We define a graded multiplication on the vector space of essential paths on a graph $G$ (a tree) and show that it is associative. In most interesting applications, this tree is an ADE Dynkin diagram. The vector space of length preserving…

In this paper, we show that for a graph $\Gamma$ from a class named H-rigid graphs, its subgraph ${\rm Int}(\Gamma)$, named the internal graph of $\Gamma$, is an isomorphism invariant of the graph product of hyperfinite II$_1$-factors…

A result of Baumslag and Roseblade states that a finitely presented subgroup of the direct product of two free groups is virtually a direct product of free groups. In this paper we generalise this result to the class of cyclic subgroup…

Given a group $G$ and an automorphism $\varphi$ of $G$, two elements $x, y \in G$ are said to be $\varphi$-conjugate if $x = g y \varphi(g)^{-1}$ for some $g \in G$. The number of equivalence classes is the Reidemeister number $R(\varphi)$…

Graph product structure theory expresses certain graphs as subgraphs of the strong product of much simpler graphs. In particular, an elegant formulation for the corresponding structural theorems involves the strong product of a path and of…

We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group…

In this paper we study the elementary theory of graph products of groups and show that under natural conditions on the vertex groups we can recover (the core of) the underlying graph and the associated vertex groups. More precisely, we…

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a…

We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if $\mathcal{F}$ is a finite collection of pairwise distinct simple closed curves on a finite type surface and if $N$ denotes the…

This paper deals with the Cayley graph $\mathrm{Cay}(\mathrm{Sym}_n,T_n),$ where the generating set consists of all block transpositions. A motivation for the study of these particular Cayley graphs comes from current research in…