One of the main examples of Artin groups are braid groups. We can use powerful topological methods on braid groups that come from the action of braid on the curve complex of the n-puctured disk. However, these methods cannot be applied in general to Artin groups. In this talk we explain how we can construct a complex for Artin groups, which is an analogue to the curve complex in the braid case, by using parabolic subgroups.
20F36 ; 20F65 ; 57M07