27 citations · 122 across the 44 of their papers we have counts for
7 papers · 1 filter
Groups acting on quasi-median graphs. An introduction
Anthony Genevois
Quasi-median graphs have been introduced by Mulder in 1980 as a generalisation of median graphs, known in geometric group theory to naturally coincide with the class of CAT(0) cube…
Cubical-like geometry of quasi-median graphs and applications to geometric group theory
Anthony Genevois
The class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometri…
Partially CAT(-1) groups are acylindrically hyperbolic
Anthony Genevois, Arnaud Stocker
In this paper, we show that, if a group acts geometrically on a geodesically complete CAT(0) space which contains at least one point with a CAT(-1) neighborhood, then m…
Hyperbolicities in CAT(0) cube complexes
Anthony Genevois
This paper is a survey dedicated to the following question: given a group acting on some CAT(0) cube complex, how to exploit this action to determine whether or not the group is Gr…
Embeddings into Thompson's groups from quasi-median geometry
Anthony Genevois
The main result of this article is that any braided (resp. annular, planar) diagram group splits as a short exact sequence where is a subgroup o…
Algebraic characterisation of relatively hyperbolic special groups
Anthony Genevois
This article is dedicated to the characterisation of the relative hyperbolicity of Haglund and Wise's special groups. More precise, we introduce a new combinatorial formalism to st…
Lamplighter groups, median spaces, and Hilbertian geometry
Anthony Genevois
From any two median spaces , we construct a new median space , referred to as the diadem product of and , and we show that this construction is compati…