Large-type Artin groups are systolic. (English) Zbl 07194965

Huang, Jingyin; Osajda, Damian

Proc. Lond. Math. Soc. (3) 120, No. 1, 95-123 (2020).

Summary: We prove that Artin groups from a class containing all large-type Artin groups are systolic. This provides a concise yet precise description of their geometry. Immediate consequences are new results concerning large-type Artin groups: biautomaticity; existence of \(E Z\)-boundaries; the Novikov conjecture; descriptions of finitely presented subgroups, of virtually solvable subgroups, and of centralizers of elements; the Burghelea conjecture; existence of low-dimensional models for classifying spaces for some families of subgroups.

MSC:

20F65	Geometric group theory
20F36	Braid groups; Artin groups
20F67	Hyperbolic groups and nonpositively curved groups