24 citations · 111 across the 23 of their papers we have counts for
28 papers
A Deligne complex for virtual Artin groups
Federica Gavazzi, Alexandre Martin
Virtual Artin groups were recently introduced by Bellingeri-Paris-Thiel as a generalisation of virtual braid groups. In this article, we initiate a geometric study of these groups…
Homomorphisms between XL-type Artin groups
Martín Blufstein, Alexandre Martin, Nicolas Vaskou
We study homomorphisms between XL-type Artin groups and show that, in a suitable sense, a generic Artin group is both hopfian and co-hopfian. For XL-type Artin groups over complete…
Acylindrical hyperbolicity for Artin groups with a visual splitting
Ruth Charney, Alexandre Martin, Rose Morris-Wright
We establish a criterion that implies the acylindrical hyperbolicity of many Artin groups admitting a visual splitting. This gives a variety of new examples of acylindrically hyper…
Characterising large-type Artin groups
Alexandre Martin, Nicolas Vaskou
We show that the class of large-type Artin groups is invariant under isomorphism, in stark contrast with the corresponding situation for Coxeter groups. We obtain this result by pr…
The Tits Alternative for two-dimensional Artin groups and Wise's Power Alternative
Alexandre Martin
We show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative: their subgroups either contain a non-abelian free group or are virtually free abelian of…
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…