4 papers · 2 filters
Smallest quotients and profinite rigidity of irreducible spherical type Artin groups
Federica Gavazzi, Igor Haladjian, Luis Paris
We prove that irreducible spherical type Artin groups are profinitely rigid within the class of all spherical type Artin groups. As part of the proof, building on ideas of Kolay fo…
A cube complex for virtual Artin groups
Jos{é} Galvez Mateos, José Galvez Mateos, Luis Paris
Let be a Coxeter graph, and let be its vertex set. An elemental complex over is an abstract simplicial complex on that contains every pair w…
Classification of Artin groups admitting retractions onto their parabolic subgroups
Bruno Aarón Cisneros de la Cruz, María Cumplido, Islam Foniqi +1
We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient…
Parabolic subgroups and word problem in virtual Artin groups
José Gálvez Mateos, Federica Gavazzi, Luis Paris
We begin by establishing two fundamental results on standard parabolic subgroups of virtual Artin groups. We first show that a standard parabolic subgroup is naturally isomorphic t…