27 citations · 122 across the 44 of their papers we have counts for
8 papers · 1 filter
Negative curvature in graph braid groups
Anthony Genevois
In this article, we initiate a geometric study of graph braid groups. More precisely, by applying the formalism of special colorings introduced in a previous article, we determine…
Morphisms between right-angled Coxeter groups and the embedding problem in dimension two
Anthony Genevois
In this article, given two finite simplicial graphs and , we state and prove a complete description of the possible morphisms between the right-angle…
Quasi-isometrically rigid subgroups in right-angled Coxeter groups
Anthony Genevois
In the spirit of peripheral subgroups in relatively hyperbolic groups, we exhibit a simple class of quasi-isometrically rigid subgroups in graph products of finite groups, which we…
A note on torsion subgroups of groups acting on finite-dimensional CAT(0) cube complexes
Anthony Genevois
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…
Rank-one isometries of CAT(0) cube complexes and their centralisers
Anthony Genevois
If is a group acting geometrically on a CAT(0) cube complex and if is an infinite-order element, we show that exactly one of the following situations occurs: (i)…
Conjugating automorphisms of graph products: Kazhdan's property (T) and SQ-universality
Anthony Genevois, Olga Varghese
An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when th…
On the geometry of van Kampen diagrams of graph products of groups
Anthony Genevois
In this article, we propose a geometric framework dedicated to the study of van Kampen diagrams of graph products of groups. As an application, we find information on the word and…
Median sets of isometries in CAT(0) cube complexes and some applications
Anthony Genevois
In this article, we associate to isometries of CAT(0) cube complexes specific subspaces, referred to as \emph{median sets}, which play a similar role as minimising sets of semisimp…