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XXL type Artin groups are CAT(0) and acylindrically hyperbolic
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We describe a simple locally CAT(0) classifying space for XXL type Artin groups (with all labels at least
5
). Furthermore, when the Artin group is not dihedral, we describe a rank
1
periodic geodesic, thus proving that XXL type Artin groups are acylindrically hyperbolic. Together with Property RD proved by Ciobanu, Holt and Rees, the CAT(0) property implies the Baum–Connes conjecture for all XXL type Artin groups.
Title: XXL type Artin groups are CAT(0) and acylindrically hyperbolic
Description:
We describe a simple locally CAT(0) classifying space for XXL type Artin groups (with all labels at least
5
).
Furthermore, when the Artin group is not dihedral, we describe a rank
1
periodic geodesic, thus proving that XXL type Artin groups are acylindrically hyperbolic.
Together with Property RD proved by Ciobanu, Holt and Rees, the CAT(0) property implies the Baum–Connes conjecture for all XXL type Artin groups.
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