10 papers
Homotopy types of complexes of hyperplanes in quasi-median graphs and applications to right-angled Artin groups
Carolyn Abbott, Anthony Genevois, Eduardo Martinez-Pedroza
In this article, we prove that, given two finite connected graphs and , if the two right-angled Artin groups and are quasi-isometric, then the infi…
Rotation groups, mediangle graphs, and periagroups: a unified point of view on Coxeter groups and graph products of groups
Anthony Genevois
In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algeb…
Examples of cubulable groups with fixed-point properties
Anthony Genevois
For every , let denote the fixed-point property for median graphs of cubical dimension (or equivalently, for CAT(0) cube complexes of dimension )…
Beyond graph products and cactus groups: quandle products of groups
Anthony Genevois
In this paper, we introduce and initiate the study of quandle products of groups, a family of groups that includes graph products of groups, cactus groups, wreath products, and the…
Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups
Laura Ciobanu, Anthony Genevois
In this article we construct contracting elements in the standard Cayley graphs of the so-called periagroups, a family of groups introduced by the second-named author which include…
Cyclic hyperbolicity in CAT(0) cube complexes
Anthony Genevois
It is known that a cocompact special group does not contain if and only if it is hyperbolic; and it does not contain $\mathbb{F}_2 \times \mathbb…