4 papers · 1 filter
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
MartÃn 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…
A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups
Jason Behrstock, Mark Hagen, Alexandre Martin +1
We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotient…
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…