Extra large type Artin groups are CAT(0) and acylindrically hyperbolic

Thomas Haettel (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

We describe a simple locally CAT(0) classifying space for extra large type Artin groups. Furthermore, when the Artin group is not dihedral, we describe a rank 1 periodic geodesic, thus proving that extra large type Artin groups are acylindrically hyperbolic. Together with Property RD proved by Ciabonu, Holt and Rees, the CAT(0) property implies the Baum-Connes conjecture for all extra large type Artin groups.

Domaines: Topologie géométrique [math.GT]

Thomas Haettel. Extra large type Artin groups are CAT(0) and acylindrically hyperbolic. 2019. ⟨hal-02157743⟩