1 citations · 1 across the 3 of their papers we have counts for
7 papers · 1 filter
Extra-large type Artin groups are hierarchically hyperbolic
Mark Hagen, Alexandre Martin, Alessandro Sisto
We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This implies in particular that these gr…
Parabolic subgroups of large-type Artin groups
María Cumplido, Alexandre Martin, Nicolas Vaskou
We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of…
Tits alternative for Artin groups of type FC
Alexandre Martin, Piotr Przytycki
Given a group action on a finite-dimensional CAT(0) cube complex, we give a simple criterion phrased purely in terms of cube stabilisers that ensures that the group satisfies the s…
Acylindrical actions for two-dimensional Artin groups of hyperbolic type
Alexandre Martin, Piotr Przytycki
For a two-dimensional Artin group whose associated Coxeter group is hyperbolic, we prove that the action of on the hyperbolic space obtained by coning off certain subcomple…
Automorphisms of graph products of groups from a geometric perspective
Anthony Genevois, Alexandre Martin
This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups…
A combination theorem for combinatorially non-positively curved complexes of hyperbolic groups
Alexandre Martin, Damian Osajda
We prove a combination theorem for hyperbolic groups, in the case of groups acting on complexes displaying combinatorial features reminiscent of non-positive curvature. Such comple…